CPM Homework Help : AC Problem 10-54

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Home > AC > Chapter 10 > Lesson 10.2.1 > Problem 10-54

10-54.

Solve the inequalities below. Write each solution as an inequality.

$8+3x>2$
Hint 1(a):
Change the inequality to an equation and solve for $x$ .
$\begin{aligned} 8 + 3x &= 2 \\ 3x &= -6 \\ x &= -2 \end{aligned}$
Hint 2(a):
Test both sides of the boundary point.
$8+3\left(-3\right)>28+3\left(-1\right)>2$
$8-9>28-3>2$
$-1>25>2$
False True
Answer (a):
$x>-2$

$\frac{2}{3}x-6\le2$
Hint (b):
Follow the steps in part (a).
Answer (b):
$x\le12$

$-2x-1<-3$
Hint (c):
Follow the steps in part (a).

$\frac{5}{x}\le\frac{1}{3}$
Hint (d):
Follow the steps in part (a).
Answer (d):
$x\ge15$

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