250 Equations and InequalitiesSolve _d 2 > 7.
_d
2 >^7 Write the inequality.(^2) (_d 2 ) > 2 (7) Multiply each side by 2.
d > 14 Simplify.
The solution is d > 14. You can check this solution by substituting
a number greater than 14 into the inequality.
a. 4 x < 40 b. 6 ≥ _x 7
Multiplication and Division Properties
of Inequality, Negative Number
Words When you multiply or divide each side of an inequality by a
negative number, the inequality symbol must be reversed
for the inequality to remain true.
Symbols For all numbers a, b, and c, where c < 0,
- if a > b, then ac < bc and a_c < _bc.
- if a < b, then ac > bc and a_c > _bc.
Examples 7 > 1 - 4 < 16- 2 (7) < - 2 (1) Reverse the symbols. --^44 > -^164
- 14 < -2 1 > - 4
These properties are also true for a ≥ b and a ≤ b.Multiply or Divide by a Negative Number
Solve _-x 3 ≤ 4. Graph the solution set on a number line.
_x
3 ≤^4 Write the inequality.
(^3) (_-x 3 ) ≥ - 3 (4) Multiply each side by -3 and reverse the symbol.
x ≥ - 12 Simplify.
Graph the solution, x ≥ -12.
16 - 14 - 12 - 10 - 8 - 6
c. _-k 2 < 9 d. - 6 a ≥ - 78
Reading Math Reading Math The
inequality c < 0 means
that c is a negative number.242_253_C04L4_895130.indd 250 12/31/09 4:06 PM