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

## Example Questions

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### Example Question #121 : Equations / Inequalities

Solve for :

Explanation:

can be simplified to become

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

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

### Example Question #1 : Linear Equations

Solve for :

Explanation:

To solve for , you must first combine the 's on the right side of the equation. This will give you .

Then, subtract  and from both sides of the equation to get .

Finally, divide both sides by  to get the solution .

### Example Question #11 : Linear / Rational / Variable Equations

Solve for :

Explanation:

First, combine like terms within the equation to get

.

Then, add  and subtract  from both sides to get

.

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

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

Solve for .

Cannot be determined

Explanation:

Subtract x from both sides of the second equation.

Divide both sides by  to get .

Plug in y to the other equation.

Divide 10 by 5 to eliminate the fraction, yielding .

Distribute the 2 to get .

Add  to each side, and subtract 15 from each side to get .

Divide both sides by 7 to get , which simplifies to .

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

Solve for :

Explanation:

Combine like terms on the left side of the equation:

Use the distributive property to simplify the right side of the equation:

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

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

Solve for :

Explanation:

First. combine like terms to get

.

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

This gives you .

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

### Example Question #151 : Equations / Inequalities

Solve for :

Explanation:

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

This gives you .

Next, subtract  from both sides to get .

Then, divide both sides by  to get .

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

Solve for

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

Next, we need to subtract  from each side:

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

Solve for

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

Next, we need to subtract  from each side:

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

Solve for

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

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

Finally, we can divide  by both sides:

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