Page 695 - Algebra 1

Example
3
Solving Inequalities with Two Operations Inside Absolute-Value Symbols
Subtract 12 from each side. Write as a compound inequality.
Add 2 to each side of the two inequalities. Multiply each side by 3 in both inequalities.
0 10 20 30
Math Reasoning
Verify For Example
3a, choose an x-value between -15 and 27. Show that it is a solution of the original inequality.
Solve and graph each inequality. a. _x-2+12≤19
⎪3 ⎥ SOLUTION
_x-2 +12≤19 ⎪3 ⎥
_x - 2 ≤ 7 ⎪3 ⎥
_x - 2 ≥ -7 AND _x - 2≤ 7 33
_x ≥ -5 AND _x ≤ 9 33
x ≥ -15 AND -15 ≤ x ≤ 27
b. ⎢2x+1 +5≥8
SOLUTION
⎢2x + 1 + 5 ≥ 8 ⎢2x + 1 ≥ 3
x ≤ 27
-20 -10
Subtract 5 from each side.
2x + 1 ≤ -3 OR 2x + 1 ≥ 3 Write as a compound inequality.
2x ≤ -4 OR 2x ≥ 2 Subtract 1 from each side of both inequalities. x ≤ -2 OR x ≥ 1 Divide each side by 2 in both inequalities.
-6 -4 -2 0 2 4 6
Application: Basketball
NCAA rules require that the circumference c of a basketball used in
an NCAA men’s basketball game vary no more than 0.25 inch from 29.75 inches. Write and solve an absolute-value inequality that models the acceptable circumferences. What is the least acceptable circumference?
SOLUTION
The expression ⎢c - 29.75 represents the difference between the actual circumference and 29.75 inches. The absolute-value bars ensure that the difference is a positive number. The difference can be no more than 0.25 inches, so the acceptable circumference is modeled ⎢c - 29.75 ≤ 0.25.
⎢c - 29.75 ≤ 0.25
-0.25 ≤ c - 29.75 ≤ 0.25 Write a compound inequality.
29.5 ≤ c ≤ 30 Add 29.75 to each side. The least acceptable circumference is 29.5 inches.
Example
4
Hint
Look for a value that varies by some amount. The absolute-value expression will be
=, ≥, or ≤ the amount by which the value varies.
680 Saxon Algebra 1