Chapter 10: Solving Equations and Inequalities 131Solving Inequalities
Inequalities can be solved in much the same way as equations, with one important exception.
When you multiply or divide both sides of an inequality by a negative number, the direction of
the inequality sign reverses. Remember that the positive and negative sides of the number line
are mirror images of one another. When you multiply both sides of the inequality by a negative
number, you go through the looking glass and things change. On the positive side, 5 is bigger
than 4, but flip to the negative side and -5 is smaller than -4.
The rules for solving inequalities are the same as those for solving equations, except for that one
step. When you multiply or divide both sides of an inequality by the coefficient of the variable
term, you have to make a decision about the inequality sign.
If you divide both sides of an inequality by a positive number, leave the inequality sign as is.If you divide both sides of an inequality by a negative number, reverse the inequality sign.3522
327
3
327
3
≥ 9≥≥≥
x 5 5
x
xx(^211)
xx
x
x
x
xx^52
25 2
27
2
2
5 5
This will flipbecause we
divide by a negative
7
2
x 3.5
≤≥≤≤≤----- 11
1 - 2 2
2 2CHECK POINT
Solve each inequality.- 2x – 5 > 13 + 4x
- 3x + 2 e 8 x + 22
- 12x + 3 < x + 36
24. 2y – 13 u 4(2 + y)
25. 5x – 10(x – 1)> 95