Answer:
22 minutes
Step-by-step explanation:
The number of minutes and number of people are inversely proportional but the number of people, minutes painted and walls painted are directly proportional. Therefore, it takes 10 people 22 / 10 = 2.2 minutes to paint 1 wall and 2.2 * 14 = 30.8 minutes to paint 14 walls. To find the time it takes 14 people to paint 14 walls, we can set up the following equation:
14 * x = 30.8 * 10 (where x is our answer)
x = 30.8 * 10 / 14 = 22 minutes
Additionally, an easier way to do this is to recognize that 1 person paints 1 wall when 10 people paint 10 walls in 22 minutes so as long as the number of people and walls are the same, it will always take 22 minutes.
perimeter help please quick !
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.4}}}}}[/tex]
Step-by-step explanation:
Given,
Length of the rectangle ( l ) = 3x + 5
Breadth of the rectangle ( b ) = 2x - 1
Perimeter of the rectangle ( P ) = 52
Finding the value of x
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]
⇒[tex] \sf{52 = 2(3x + 5 + 2x - 1)}[/tex]
⇒[tex] \sf{52 = 2(5x + 4)}[/tex]
⇒[tex] \sf{52 = 10x + 8}[/tex]
⇒[tex] \sf{10x + 8 = 52}[/tex]
⇒[tex] \sf{10x = 52 - 8}[/tex]
⇒[tex] \sf{10x = 44}[/tex]
⇒[tex] \sf{ \frac{10x}{10} = \frac{44}{10} }[/tex]
⇒[tex] \sf{x = 4.4 \: }[/tex]
Hope I helped!
Best regards!! :D
Louisa states that the solution to the equation One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4 is x = 56. She verifies her solution using the steps below.
Equation: One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4
Step 1: One-fourth (56) minus 3 = StartFraction 3 Over 8 EndFraction (56) + 4
Step 2: 14 minus 3 = 21 + 4
Step 3: 11 = 25
Answer:
A
Step-by-step explanation:
The answer is A
Factor 25 - 4x^2
25 – 4x^2 = 0
Answer: (5 + 2x)(5 - 2x)
Step-by-step explanation:
It seems a bit backwards from the way these are usually set up, but still it is the difference of two perfect squares.
Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?
Answer:
64 poles
Step-by-step explanation:
Given the question :
Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?
Dimension of rectangular field = 100m by 60m
Length = 100m ; breadth = 60m
Since it is erected around the corners of the field, we need to calculate the entire perimeter of the rectangular field.
Perimeter of a rectangle : 2( length + breadth)
Perimeter = 2(100 +60) = 2(160) = 320m
Since the posts are erected 5m apart, the number of post needed will be :
Perimeter / 5
= 320 / 5
= 64 poles
How can you prove that a conjecture if false?
Answer:
To show that a conjecture is false, you have to find only one example in which the conjecture is not true. So an example could be a drawing, a statement, or a number.
The polynomial expressions 10x2 + 26x – 12 and 2(5x – 2)(x – 3) share a common binomial factor.
What binomial factor do they share?
Answer:
(5x-2)
Step-by-step explanation:
first factor the quadratic equation
10x²+26x-12 by factoring out the gcf of 2
2(5x²+13x-6) to factor the quadratic, first multiply ac (5)(-6)
find factors of -30 that multiply to give you -30 and add to give you the middle term 13.
factors -2, 15
take your leading term 5x and put it over the 2 factors, then reduce when necessary. it is not necessary to use the 5x² because the x in the denominator cancels one out)
5x/-2 and 5x/15 (this one can be reduced to x/3
(5x-2)(x+3) are the factors.
the shared factor is (5x-2)
Answer:
they share 5x-2 as common factor
Step-by-step explanation:
10x² + 26x – 12 and 2(5x – 2)(x – 3)
10x² + 26x – 12 take 2 as common factor
2(5x²+13x-6) factorize
2(5x-2)(x+3)
they share 5x-2 as common factor
Find the difference. 15 5/12 - 11 1/8
Answer:
4 7/24
Step-by-step explanation:
Answer:
103/24 or 4.29 or 4 7/24
Step-by-step explanation:
15 5/12 - 11 1/8
185/12 - 89/8
370/24 - 267/24 = 103/24
or
15 10/24 - 11 3/24 = 4 7/24
find the inverse of the function f(x)=6x^2+3
Answer:
The answer is
[tex]{f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Step-by-step explanation:
f(x) = 6x² + 3
To find the inverse of the function above equate it to y
That's
f(x) = y
So we have
y = 6x² + 3
Next interchange the variables that's x becomes y and y becomes x.
x = 6y² + 3
Next make y the subject
Subtract 3 from both sides
That's
6y² + 3 - 3 = x - 3
6y² = x - 3
Divide both sides by 6
That's
[tex] {y}^{2} = \frac{x - 3}{6} [/tex]Next find the square root of both sides
[tex]y = \sqrt{ \frac{x - 3}{6} } [/tex]We have the final answer as
[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x - 3}{6} } [/tex]Hope this helps you
Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$, and $D$ are integers, $D$ is positive, and $B$ is not divisible by the square of any prime. Find the minimum possible value of $A+B+C+D$.
Rationalizing the denominator involves exploiting the well-known difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
We have
[tex](\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14[/tex]
so that
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}[/tex]
Rewrite 16 and 32 as powers of 2, then simplify:
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}[/tex]
[tex]\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7[/tex]
So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.
The rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Rationalizing SurdsFrom the question, we are to rationalize the denominator of the given surd.
We are to write the answer in the form
[tex]\frac{A\sqrt{B}+C}{D}[/tex]
and find the minimum possible value of A + B + C + D
The given surd is
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}[/tex]
To rationalize the surd, we will multiply the numerator and denominator by the conjugate of the denominator
The conjugate of the denominator is [tex]\sqrt{16}+\sqrt{2}[/tex]
Therefore,
[tex]\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \times \frac{\sqrt{16}+\sqrt{2}}{\sqrt{16}+\sqrt{2}}[/tex]
[tex]= \frac{\sqrt{32}(\sqrt{16}+\sqrt{2})}{(\sqrt{16}-\sqrt{2})(\sqrt{16}+\sqrt{2})}[/tex]
[tex]= \frac{\sqrt{512}+\sqrt{64})}{(\sqrt{16})^{2} -(\sqrt{2})^{2} }[/tex]
[tex]= \frac{16\sqrt{2}+8}{16-2}[/tex]
[tex]= \frac{16\sqrt{2}+8}{14}[/tex]
[tex]= \frac{2(8\sqrt{2}+4)}{2(7)}[/tex]
By comparing with, [tex]\frac{A\sqrt{B}+C}{D}[/tex]
A = 8, B = 2, C = 4, and D = 7
Then, the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
Hence, the rationalized form of the given surd is [tex]\frac{8\sqrt{2}+4}{7}[/tex], and the minimum possible value of A + B + C + D = 8 + 2 + 4 + 7 = 21
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Does 21, 10, and 9 be the measures of the sides of a triangle
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
9+10 > 21
19 >21
This is not true so it cannot make a triangle
How would you combine like terms with exponents? Do you add the exponents?
Answer: When combining like terms, add or subtract the coefficients. Keep the exponents as they are.
Step-by-step explanation:
You can combine 2x^2 + 3x^2 to get 5x^2. If x =3, 3^2=9 So 2(3)^2 is 18 and 3(3)^2 is 27. 18+27=45 And 5(3)^2= 45. Same result!
You can not combine 2x^2 and 2x^3. If the value of x is 3, 2(3)^2 this term works out to =18 and 2(3)^3 =54
If you add the exponents x^5 becomes 2(3)^5 or 2×243=486. Vastly different values! Don't add exponents unless you are multiplying terms.
Yes, when combining like terms with exponents, you add the exponents only if the terms have the same base.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
When combining like terms with exponents, you add the exponents only if the terms have the same base.
For example,
3x² + 9x²
= (3 + 9)x²
= 12x²
And,
2² x 2³
= [tex]2^{2 + 3}[/tex]
= [tex]2^5[/tex]
Thus,
Yes, we add the exponents.
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On a coordinate plane, point M is plotted (-3,-1) and point N is plotted (4,5). What is the distance between points M and N? square root of 117 square root of 85 5 square root of 17 85
Answer:
The square root of 85
Step-by-step explanation:
The formula to find out the distance between the points is shown below:
The Distance is
[tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
where,
x_1 = -3
y_1 = -1
x_2 = 4
And, the y_2 = 5
Now place these values to the above formula
So, the distance is
[tex]= \sqrt{(4+3)^2 + (5+1)^2} \\\\= \sqrt{49 + 36} \\\\= \sqrt{85}[/tex]
= 9.22 units
Hence, the distance between points M and N is 9.22 units or the square root of 85
Hence, the second option is correct
HELP PLEASE
Will give brainliest
Answer:
[tex]=7x^2+8x-2[/tex]
Step-by-step explanation:
So, on Monday, Tuesday, and Wednesday, he mowed:
[tex](4x^2+3x-4),(5x-8),(3x^2+10)[/tex]
yards, respectively.
To determine how many yards he mowed in the three days, simply add the three expressions. Thus:
[tex](4x^2+3x-4)+(5x-8)+(3x^2+10)[/tex]
Combine like terms:
[tex]=(4x^2+3x^2)+(3x+5x)+(-4-8+10)[/tex]
Add or subtract:
[tex]=7x^2+8x-2[/tex]
And it cannot be simplified further :)
The chart shows the cost of tuition at a certain state university. Model the data in the chart with a linear function, using the points (1,9941) and (3,11242). Predict the cost of college tuition in 2007-2008.
What is the linear model for the data?
Y=?
Answer:
The cost in 2007 - 2008 = $15,795.5
The linear model for the data is y = $650.5·x + $9290.5
Step-by-step explanation:
The given data can be presented as follows;
College year, x, Estimated tuition, y
1997-1998, 0, $9412
1998-1999, 1, $9941
1999-2000, 2, $10561
2000-2001, 3, $11242
2001-2002, 4, $11965
2002-2003, 5,
2003-2004, 6,
2004-2005, 7,
2005-2006, 8,
2006-2007, 9,
2007-2008, 10,
With points (1, 9941) and (3, 11242), we have the slope given by the equation;
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Which gives;
[tex]m = \dfrac{11242 - 9941}{3 - 1}= 650.5[/tex]
Therefore;
y - 11242 = 650.5 × (x - 3)
y= 650.5·x - 650.5 ×3 + 11242
y = 650.5·x + 9290.5
Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;
y = 650.5×10 + 9290.5 = $15,795.5
The cost (estimated tuition) in 2007 - 2008 = $15,795.5
The linear model for the data is y = 650.5·x + 9290.5.
The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5
Linear equationA linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let y represent the cost of tuition of battery after x years.
From the table using the points (1, 9941) and (3, 11242):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5[/tex]
The linear model for the data is y = 650.5x + 9290.5
At 2007-2008 (x = 10:
y = 650.5(10) + 9290.5 = 15795.5
The cost of college tuition in 2007-2008 is $15795.5
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A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Answer:
20360.16 cm^3Step-by-step explanation:
We are going to assume that the cylinder is filled with water to the brim
Given that the data of the cylinder is
height h= 180 cm
radius r= 60 cm
The formula for the volume of a cylinder is
[tex]volume= \pi r^2h[/tex]
[tex]volume = 3.142*60^2*180\\\\volume= 3.142*3600*180\\\\volume= 20360.16 cm^3[/tex]
The volume of water in the cylinder is 20360.16 cm^3
What is the simplified form of each expression? (6 + 3)^2 - 4
Answer:
77
Step-by-step explanation:
(6 + 3)² is same as (a + b)²
Since (a + b)² = a² + 2ab + b²
Therefore,
(6 + 3)² - 4
= (36 + 36 + 9) - 4
= 81 - 4
= 77
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------
Answer: [tex]\boxed{77}[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Since PEMDAS exists, we will do parentheses "(6+3)" first to get 9.
Then we do the exponent which is:
[tex]9^{2}[/tex] = 81.
Then we subtract.
81 - 4 = 77.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
More broken down explanation:
[tex](6+3)^{2} -4[/tex]
Add 6 and 3 to get 9.
[tex]9^{2} - 4[/tex] ≈ [tex]77[/tex]
Calculate 9 to the power of 2 and get 81.
[tex]81-4[/tex] = [tex]77[/tex]
Subtract 4 from 81 to get, you guessed it, 77!A sixth-grade class went on a field trip. There were 24 chaperones and 84 students on the trip. What is the ratio of chaperones to total people who went on the trip? *
Answer:
24 : 84 = 2 : 7
Step-by-step explanation:
We can simplify the ratio 24 : 84 by dividing both terms by the greatest common factor (GCF).
The GCF of 24 and 84 is 12.
Divide both terms by 12.
24 ÷ 12 = 2
84 ÷ 12 = 7
Therefore:
24 : 84 = 2 : 7
Do the ratios 20/10 and 1/2 form a proportion?
Answer:
Yes . Divide by 10 for 10/20 to get 1/2.
10/10= 1
20/10= 2
10/20= 1/2
if k is the midpoint of LM and k (-4,-6) and m(-7,-3). find l (endpoint)
Answer:
(-1,-9) PLEASE MARK BRAINLIEST!!!!!
Step-by-step explanation:
k(-4,-6) , m(-7,-3)
-7+4=-3
-3+6=3
-4+3=-1
-6-3=-9
(-1,-9)
The coordinate of L is (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
if k is the midpoint of LM and k (-4,-6) and m(-7,-3).
It is required to find the coordinate of L:
Using the mid-point theorem:
Let the coordinate of L is (x, y)
(x - 7)/2 = -4
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
x - 7 = -8
x = -8 + 7
x = -1
(y - 3)/2 = -6
y - 3 = -12
y = -12 + 3
y = -9
The coordinate of L is (-1,-9)
Thus, the coordinate of L is (-1,-9) if the k is the midpoint of LM and k (-4,-6) and M (-7,-3).
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Two sides of a triangle are equal in length and double the length of the shortest side. The perimeter of the triangle is 36 inches.
Answer:
Two equal sides = 14.4 inches each
Shortest side = 7.2 inches
Step-by-step explanation:
a + b + c = 36
a = b
a = 2c
then:
c = a/2
a + a + a/2 = 36
2a + a/2 = 36
4a/2 + a/2 = 36
5a/2 = 36
a = 2*36/5
a = 72/5
a = 14.4
a = 2c
14.4 = 2*c
c = 14.4/2
c = 7.2
a = b
b = 14.4
Check:
14.4 + 14.4 + 7.2 = 36
Max spent $15 on bowling. This included a $5 charge for shoe rental and a $2.50 charge per game. If g represents the number of games, which equation can be solved to find the number of games that Max bowled?
Answer:
Step-by-step explanation:
$2.50g + $5 = $15
$2.50g = 10
g = 4 games
The equation that is used to find the number of games that Max bowled is [tex]5+2.50x=15.[/tex]
Charge for shoe rental [tex]=[/tex] $[tex]5[/tex].
Charge per game [tex]=[/tex] $[tex]2.50[/tex].
Let [tex]g[/tex] represents the number of games.
The total charge is the sum of shoe rental charge and charge per game times the number of games.
Total money spent [tex]=[/tex] $[tex]15[/tex].
[tex]5+2.50x=15[/tex]
This is the equation that is used to find the number of games that Max bowled.
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Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5) (x=3)
(X+5) (x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
b. What is the radius of a ball that uses one-half of the amount of rubber coating used to cover the 16-inch ball? Write your answer in simplest form.
The radius is
inches.
Question 2
A playground ball with a 16-inch diameter has a rubber coating on its surface.
a. Does a ball with a diameter that is $\frac{1}{4}$
times the diameter of the given ball need $\frac{1}{4}$
times the amount of rubber coating? Explain.
Answer:
The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball is approximately 4.66 inches
Step-by-step explanation:
The dimension of the ball with known radius = 16-inch
The surface area of the ball with 16-inch radius = 4×π×r² = π·D² = π×16² = 804.24772 in.²
Given that the ball uses one-half the rubber material coating used to cover the 16-inch ball, we have the surface area of the ball = 804.24772 in.²/2 = 402.12386 in.²
The radius, r₂ of the new ball is found as follows;
402.12386 in.² = 4×π×r₂²
r₂² = 402.12386 in.² /(4×π) ≈ 32
r₂ = √32 = 4·√2 ≈ 4.66 inches
The radius, r₂, of the ball that uses one-half the amount of rubber coating used to cover the 16-inch ball ≈ 4.66 inches.
Math Do Now: Maria has a coupon for 30% at Kohl's. If she purchases $200 worth
of clothes, what is her total before taxes? *
Please help me!! I can't do this...
Answer:
focus and belive on your self
Step-by-step explanation:
On Saturday, a local hamburger shop sold a combined total of 404 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer:134.7
Step-by-step explanation:
Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy? A.162 A. 162 B.163 B. 163 C.166 C. 166 D.167 D. 167
Answer:
Option B, 163 caps.
Step-by-step explanation:
The price of caps are = $6 per cap.
Shipping charge = $25
The total budget of the Laura = $1000
Since the $25 is shipping charge so subtract it from the budget = 1000 – 25 = $975
Here $975 will be used to buy the caps at the price of $6 per cap.
Thus, the number of caps = budget after subtracting the shipping fee / per cap price
Total caps = $975 / 6
Total caps = 162.5 or 163 caps.
Plz help ASAP!!!! WILL MARK YOU BRAINLIST IF YOUR ANSWER IS CORRECT!! Question # 7 last question
Answer:
the last one
Step-by-step explanation:
i took the test
If you plug x = 3 into choice A, then you dont have any division by zero errors or square roots of negative values.
Choice B in contrast has x-9 = 3-9 = -6 under the square root, so this leads to an imaginary/complex result. Choice D is similar.
Choice C will have zero in the denominator after plugging in x = 3 since x^2-9 = 3^2-9 = 9-9 = 0.
14, the difference of 4 times a and b
What is "the sum of twice a number and six is the same as three subtracted from the number itself"?
Answer:
x=-1
Step-by-step explanation:
2x+6=3-x
Step 1: Simplify both sides of the equation.
2x+6=3−x
2x+6=3+(−x)
2x+6=−x+3
Step 2: Add x to both sides.
2x+6+x=−x+3+x
3x+6=3
Step 3: Subtract 6 from both sides.
3x+6−6=3−6
3x=−3
Step 4: Divide both sides by 3.
3x/3=−3/3
x=−1
Answer:
x=−1