Back to: Algebra 1

A multi-step inequality, as its name implies, is an inequality requiring more than one step to solve it. It is very similar to an equation except that when multiplying or dividing by a negative quantity the sign of inequality must be reversed.

**Example**: Solve, 16 – 8x < 48.

16 – 8x < 48

– 16 -16 *Subtract 16*

——————

– 8x < 32 **Divide by – 8**

x > -4 **Reverse the sign of inequality**

**Example**: Solve, -3y + 6 > – 21.

-3y + 6 > – 21

– 6 -6 *Subtract 6*

——————

– 3y > – 27 *Divide by – 3*

y < 9 *Reverse the sign of inequality*

**Example**: Solve, – 37 ≥ -7p + 5.

– 37 ≥ -7p + 5

– 5 – 5 **Subtract 5**

——————–

– 42 ≥ -7p **Divide by – 7**

6 ≤ p *Reverse the sign of inequality*

**Example**: Solve, 9 – 3∕4b > 15.

9 – 3∕4b > 15

– 9 – 9 **Subtract 9**

——————–

– 3∕4b > 6 *Multiply by 4*

– 3b > 24 *Divide by – 3*

b < – 8 **Reverse the sign of inequality**

**Example**: Solve, -17 ≤ – 5∕3x – 2.

-17 ≤ – 5∕3x – 2

+ 2 ≤ + 2 *Add 2*

———————-

– 15 ≤ – 5∕3x *Multiply by 3*

– 45 ≤ -5x *Divide by -5*

9 ≥ x **Reverse the sign of inequality**