# High School Math : Solving Inequalities

## Example Questions

### Example Question #1 : Solving Inequalities

Solve for :

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that  becomes , and vice versa.

### Example Question #1 : Solving Inequalities

Solve for :

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that  becomes , and vice versa. When we solve binomials, we must take extra caution because .

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.

Now we must create our two scenarios:

and

Notice that in the negative scenario, we flipped the sign of the inequality.

and

and

### Example Question #2 : Solving Inequalities

Solve for :

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that  becomes , and vice versa. When we solve binomials, we must take extra caution because .

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.

Now we must create our two scenarios:

and

Notice that in the negative scenario, we flipped the sign of the inequality.

and

and

### Example Question #51 : Basic Single Variable Algebra

Solve the inequality for x:

Explanation:

Subtract 4 from both sides:

Divide both sides by 2:

### Example Question #51 : Basic Single Variable Algebra

Solve for .

Explanation:

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

### Example Question #52 : Basic Single Variable Algebra

Solve for :

Explanation:

Move like terms to the same sides:

Combine like terms:

Divide both sides by 3:

Solve for :