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

## Example Questions

### Example Question #1 : Linear Equations

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 : How To Find The Solution To An Equation

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

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 #11 : How To Find The Solution To An Equation

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 #4 : Linear Equations

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 #3 : 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 #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

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 #5 : 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 #6 : 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:

Solve for