# Algebra 1 : Systems of Inequalities

## Example Questions

### Example Question #1 : How To Find The Solution To An Inequality With Subtraction

What is a possible valid value of ?

Explanation:

This inequality can be rewritten as:

4x + 14 > 30  OR 4x + 14 < –30

Solve each for x:

4x + 14 > 30; 4x > 16; x > 4

4x + 14 < –30; 4x < –44; x < –11

Therefore, anything between –11 and 4 (inclusive) will not work. Hence, the answer is 7.

### Example Question #5 : How To Find The Solution To An Inequality With Subtraction

Solve for .

Explanation:

First subtract 2p from both sides:

p + 5 < 12.

Then subtract 5 from both sides:

p < 7

### Example Question #6 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality.

Explanation:

Isolate the term with  on one side and the constants on the other side.

First subtract 7x on both sides and add 5 to both sides.

Next, divide by 3 to solve for x.

### Example Question #7 : How To Find The Solution To An Inequality With Subtraction

Solve for

Explanation:

To solve for the variable we need to isolate the variable on one side of the inequality and all other constants on the other side. In order to do this, perform inverse operations.

First subtracting 7 from both sides we get:

Then subtracting 2x from both sides:

Finally divide both sides by 2:

### Example Question #8 : How To Find The Solution To An Inequality With Subtraction

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 adding six to each side.

Whatever you do to one side you must also do to the other side.

This gives you:

### Example Question #9 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality:

Explanation:

In order to isolate the  variable, we will need to subtract 10 on both sides of the equation.

Simplify the left and the right side of the equation.

### Example Question #10 : How To Find The Solution To An Inequality With Subtraction

Solve for x:

Explanation:

When you are solving for an inequality, it is easiest to treat the inequality sign as an equal sign while you solve for x.

In order to solve for x, you need to get x by itself on one side. The first thing you would need to do is subtract 6 from both sides. That would leave you with . In order to get x by itself, you need to divide both sides by 9. This would bring you to the answer of .

### Example Question #31 : Systems Of Inequalities

Find the solution to the inequality:

Explanation:

In order to isolate the  variable, we need to move the 18 to the left side by subtracting 18 on both sides.

Simplify both sides.

This indicates that  must be less than or equal to negative nine.

Rewrite the inequality so that the  is on the left side, and the number is on the right side.

### Example Question #32 : Systems Of Inequalities

Solve the inequality:

Explanation:

In order to isolate the x-variable, simply subtract 13 from both sides of the inequality.

Simplify both sides of the inequality.

There is no need to switch the sign.

### Example Question #33 : Systems Of Inequalities

Solve the inequality: