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

## Example Questions

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

Solve the inequality:

Explanation:

First combine like terms on the right side of the inequality to obtain . Next, try to isolate the variable:.

The answer is therefore .

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

Solve the inequality:

Explanation:

Distribute the negative sign first:  becomes . Since there are no like-terms to combine on one side of the inequality sign, we will try to isolate the variable: . The answer is therefore

### Example Question #3 : How To Find The Solution To An Inequality With Subtraction

Which one of the following is is a valid value for ?

Explanation:

Since the inequality includes absolute value, you have two possiblities to consider: when the outcome is positive and when it is negative. When you consider the negative outcome, you must flip the inequality sign to solve for :

This means that  is less than positive 20 AND greater than negative 20:

AND

For each case, you will first subtract 4 from the left to the right. Then, you will divide both sides by 4 to isolate :

AND

AND

This gives you the interval for valid values of :

### 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 #1 : 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:

The answer, therefore, is .

### 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.

Solve for x: