Chapter 2: Q. 2.99 (page 173)

Solve each inequality, graph the solution on the number line, and write the solution in interval notation:
$a) p - \frac{3}{4} \geq \frac{1}{6} b) 9 c > 72 c) 24 \leq \frac{3}{8} m$

Short Answer

Expert verified

The solution to the given problems are:

$a) p \geq \frac{11}{12} o r p \in [\frac{11}{12}, \infty) b) c > 8 o r c \in (8, \infty) c) m \geq 64 o r [64, \infty]$

Step by step solution

Step 1. Solving Part (a).

We have

$a) p - \frac{3}{4} \geq \frac{1}{6} p \geq \frac{1}{6} + \frac{3}{4} p \geq \frac{2 + 9}{12} p \geq \frac{11}{12} \Rightarrow p \in [\frac{11}{12}, \infty)$

We show this in a number line :

Step 2. Solving Part (b).

We have

$b) 9 c > 72 c > \frac{72}{9} c > 8 o r c \in (8, \infty)$

We show this in a number line :

Step 3. Solving Part (c).

We have

$c) 24 \leq \frac{3}{8} m \frac{24 \times 8}{3} \leq m 8 \times 8 \leq m m \geq 64 o r [64, \infty]$

We show this in a number line :

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Solve each inequality, graph the solution on the number line, and write the solution in interval notation:
$a) p - \frac{3}{4} \geq \frac{1}{6} b) 9 c > 72 c) 24 \leq \frac{3}{8} m$

Short Answer

Step by step solution

Step 1. Solving Part (a).

Step 2. Solving Part (b).

Step 3. Solving Part (c).

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Solve each inequality, graph the solution on the number line, and write the solution in interval notation:a)p−34≥16b)9c>72c)24≤38m

Short Answer

Step by step solution

Step 1. Solving Part (a).

Step 2. Solving Part (b).

Step 3. Solving Part (c).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution on the number line, and write the solution in interval notation:
$a) p - \frac{3}{4} \geq \frac{1}{6} b) 9 c > 72 c) 24 \leq \frac{3}{8} m$