CPM Homework Help : CCA2 Problem C-37

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C-37.

Solve the following inequalities for $x$ . Graph your solutions on a number line.

$3x - 5 ≤ 7 + 2x$
Hint (a):
Treat the inequality sign like an equation, then solve.
$3x − 5 = 7 + 2x$
$x − 5 = 7$
$x = 12$
More Help (a):
Check a point to see which side is true.
Answer (a):
$x ≤ 12$

$|x| - 3 < 7$
Hint (b):
Solve for the absolute value of $x$ , then make two equations.
$|x| − 3 = 7$
$|x| = 10$
$x = ±10$
More Help (b):
Test numbers to determine which region is the solution.
Answer (b):
$-10 < x < 10$

$5(2 − x) + 6 > 16$
Hint (c):
Distribute, then solve for $x$ .
Answer (c):
$x > 0$

$| x + 2 | > 3$
Hint (d):
See part (b).

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