Solving multi-step inequalities is similar to solving multi-step equations, except when the coefficient of x is negative, the inequality sign must be reversed when multiplying or dividing both sides by a negative number. Some examples of correctly solving multi-step inequalities are provided.

2. Solving multi-step inequalities
is like
solving multi-step equations.
If you can solve
1132 =+x
you can solve
1132 ≤+x

3. 1132 =+x 1132 ≤+x
3− 3−
82 =x 82 ≤x
2 2
4=x 4≤x
3− 3−
2 2

4. The only time it gets tricky
is when
the coefficient of x
is negative.
2695 <−− x

5. Then you need to remember
the rule:
2695 <−− x

6. Anytime you multiply or divide
both sides of an inequality
2695 <−− x
by a negative number,
you need to reverse the sign.

7. >
The solution would look like
this:
2695 <−− x
9+ 9+
355 <− x
5− 5−
7−x

8. Solve this:
3172 ≥+x

9. Is this what you did?
3172 ≥+x
7− 7−
242 ≥x
2 2
≥ 24x

10. Try this:
1013
4
−≤−
−
x

11. Is this what you did?
1013
4
−≤−
−
x
13+ 13+
3
4
≤
−
x
( ) ( )43
4
4 −≤
−
−
x
≥ 12−x

12. Try this:
89110 −>+− x

13. Is this what you did?
1− 1−
9010 −>− x
< 9x
89110 −>+− x
10− 10−

14. One more:
1415
3
1
−<−− x

15. ( ) ( )31
3
1
3 −<




−− x
1415
3
1
−<−− x
Is this what you did?
15+ 15+
> 3−x