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

## Example Questions

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### Example Question #31 : How To Find The Solution To An Inequality With Division

Find the solution of the inequality:

Explanation:

To isolate the x-variable, we will need to divide by negative four on both sides.  This is the same as multiplying negative one fourth on both sides.

Since we have a negative in front, we will also need to switch the sign.

Simplify both sides of the equation and switch the sign.

### Example Question #32 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Divide by negative three on both sides.

Remember that since we are dividing by a negative sign, we will need to switch the sign.

### Example Question #33 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Subtract six on both sides.

Divide by negative three on both sides.  When we divide by a negative number, we will need to switch the direction of the sign.

Simplify both sides and switch the sign.

### Example Question #34 : How To Find The Solution To An Inequality With Division

Solve the following inequality:

Explanation:

Isolate the x-variable by dividing by five on both sides.  There is no need to switch the sign in this scenario.

Simplify both fraction.

### Example Question #35 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

To solve this inequality, divide both sides by negative nine.

Since we are dividing by a negative number, we will need to switch the direction of the sign.

Simplify both sides.

### Example Question #36 : How To Find The Solution To An Inequality With Division

Solve the following inequality:

Explanation:

Divide by negative twelve on both sides of the inequality.

Dividing by a negative value requires changing the direction of the sign.

Simplify both sides.

### Example Question #37 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Divide both sides by negative two.  We will need to switch the direction of the sign.

Simplify both sides and switch the sign.  Rewrite the complex fraction such that dividing by a negative two is similar to multiplying by negative half.

Multiply the fractions on the right.

### Example Question #38 : How To Find The Solution To An Inequality With Division

Solve the inequality:

Explanation:

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides.  Since we are dividing by a negative number, the sign will switch.

Simplify both sides.