# Algebra 1 : How to find the solution to an inequality with addition

## Example Questions

### Example Question #51 : Systems Of Inequalities

Solve the following inequality:

Explanation:

To solve the inequality, get all terms with  on one side and all constants on the other side. We first subtract  from both sides

,

Now add 7 to both sides

.

Now divide both sides by 2

### Example Question #61 : Equations / Inequalities

Solve this inequality:

Not enough information to be determined.

Explanation:

To solve this inequality, we need to separate the constants from the variables so that they are on opposite sides of the inequality.

We can do this by adding (4x+5) to each side and

.

The constants cancel on the left side, and the variables cancel on the right side.

Then, we divide both sides by 16, to get our final answer:

### Example Question #62 : Equations / Inequalities

Simplify the following inequality:

Explanation:

This is a one-step problem in which all you need to do is add the  to both sides to get  by itself.

So,

Then simplify to get:

### Example Question #11 : How To Find The Solution To An Inequality With Addition

Find all of the solutions to this inequality.

Explanation:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by subtracting three from each side.

Whatever operation you do to one side you must do to the other side as well.

This gives you:

### Example Question #11 : How To Find The Solution To An Inequality With Addition

Solve the inequality:

Explanation:

In order to isolate the  variable, we will need to add nine on both sides.

Simplify both sides of the equation.

### Example Question #65 : Equations / Inequalities

Solve the following inequality:

Explanation:

Add both sides by four to isolate the  variable.

Simplify both sides of the equation.

This means that  is greater than forty, but cannot equal to forty.

### Example Question #66 : Equations / Inequalities

Solve for x in the following inequality:

Explanation:

When solving an inequality, we will solve it the same way we would solve an equation.  We are solving for x, so we want x to stand alone. In the equation

we want to add 5 to both sides. The inequality symbol does not change.  We get

### Example Question #67 : Equations / Inequalities

Find the solution of the inequality:

Explanation:

To isolate the unknown variable, we will need to add 14 on both sides.

Simplify both sides of the equation.

### Example Question #68 : Equations / Inequalities

Solve the inequality:

Explanation:

In order to solve for the unknown variable, add 12 on both sides.

Simplify both sides.

### Example Question #69 : Equations / Inequalities

Find the solution: