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Common Core: 8th Grade Math : Solve Linear Equations with Rational Number Coefficients: CCSS.Math.Content.8.EE.C.7b

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Example Questions

Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

8x-5-4x=-x+10

Possible Answers:

Correct answer:

Explanation:

8x-5-4x=-x+10 can be simplified to become

4x-5=-x+10

Then, you can further simplify by adding 5 and to both sides to get 5x=15 .

Then, you can divide both sides by 5 to get x=3 .

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Example Question #2 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

6x-1=12x+8-3x

Possible Answers:

Correct answer:

Explanation:

To solve for , you must first combine the 's on the right side of the equation. This will give you $\ 6x-1=9x+8$ .

Then, subtract and from both sides of the equation to get -9=3x .

Finally, divide both sides by to get the solution x=-3 .

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Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

9x-2-2x=2x+18

Possible Answers:

Correct answer:

Explanation:

First, combine like terms within the equation to get

7x-2=2x+18 .

Then, add and subtract from both sides to get

5x=20 .

Finally, divide both sides by to get the solution of x=4 .

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Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for .

5x+15=10y

5y+x=18

Possible Answers:

x=3

x=5

Cannot be determined

x=15

y=3

Correct answer:

x=3

Explanation:

Subtract x from both sides of the second equation.

5y+x=18

5y=18-x

Divide both sides by to get $y=\frac{18-x}{5}$ .

Plug in y to the other equation.

5x+15=10y

$5x+15= 10*\frac{18-x}{5}$

Divide 10 by 5 to eliminate the fraction, yielding 5x+15=2(18-x) .

Distribute the 2 to get 5x+15=36-2x .

Add to each side, and subtract 15 from each side to get 7x=21 .

Divide both sides by 7 to get $\frac{x}{7}=\frac{21}{7}$ , which simplifies to x=3 .

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Example Question #5 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

6x-3-4x+5=3(x-1)

Possible Answers:

Correct answer:

Explanation:

Combine like terms on the left side of the equation: 2x+2=3(x-1)

Use the distributive property to simplify the right side of the equation: 2x+2=3x-3

Next, move the 's to one side and the integers to the other side: x=5

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Example Question #6 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

6x-9-x=2x-6

Possible Answers:

Correct answer:

Explanation:

First. combine like terms to get

5x-9=2x-6 .

Then, add and subtract from both sides to separate the terms.

This gives you 3x=3 .

Finally, divide both sides by to get a solution of x=1 .

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Example Question #6 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

8(x+5)=16

Possible Answers:

$\frac{11}{8}$

None of the other answers

$-\frac{11}{8}$

Correct answer:

Explanation:

First, you must multiply the left side of the equation using the distributive property.

This gives you 8x+40=16 .

Next, subtract from both sides to get 8x=-24 .

Then, divide both sides by to get x=-3 .

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Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for $x\textup:$

$\frac{x+24}{7}=4$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the to one side of the equation.

For this problem, we need to multiply each side by $7\textup:$

$7\left ( \frac{x+24}{7}\right )=4(7)$

x+24=28

Next, we need to subtract from each side:

$\frac{\begin{array}[b]{r}x+24=28\\ -24-24\end{array}}{\\\\x=4}$

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Example Question #5 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for $x\textup:$

$\frac{x+17}{3}=5$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the to one side of the equation.

For this problem, we need to multiply each side by $3\textup:$

$3\left ( \frac{x+17}{3}\right )=5(3)$

x+17=15

Next, we need to subtract from each side:

$\frac{\begin{array}[b]{r}x+17=15\\ -17-17\end{array}}{\\\\x=-2}$

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Example Question #9 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for $x\textup:$

$\frac{x+28}{3x}=5$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the to one side of the equation.

For this problem, we need to multiply each side by $3x\textup:$

$3x\left ( \frac{x+28}{3x}\right )=5(3x)$

x+28=15x

Next, we need to combine like terms, so we subtract from both sides:

$\frac{\begin{array}[b]{r}x+28=15x\\ -x\ \ \ \ \ \ \ \ \ \ -x\end{array}}{\\\\28=14x}$

Finally, we can divide by both sides:

$\frac{28}{14}=\frac{14x}{14}$

2=x

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Solve Linear Equations with Rational Number Coefficients: CCSS.Math.Content.8.EE.C.7b

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #2 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #5 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #6 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #6 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #4 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #5 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #9 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

All Common Core: 8th Grade Math Resources

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