Chapter 2: Q. 391 (page 195)

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{3}{4} (x - 8) \leq 3 a n d \frac{1}{5} (x - 5) \leq 3$

Short Answer

Expert verified

Solution of each inequalities:

$x \leq 12 a n d x \leq 20$

Graph the numbers that make both inequalities true:

The Solution in interval notation:

$(- \infty, 12]$

Step by step solution

Step 1. Given information

Consider the inequalities

$\frac{3}{4} (x - 8) \leq 3 a n d \frac{1}{5} (x - 5) \leq 3$

Step 2. Solve each inequality

$\frac{3}{4} (x - 8) \leq 3 x - 8 \leq 3 \times \frac{4}{3} x - 8 \leq 4 x \leq 4 + 8 x \leq 12$ and $\frac{1}{5} (x - 5) \leq 3 x - 5 \leq 3 \times 5 x - 5 \leq 15 x \leq 15 + 5 x \leq 20$

Step 3. Graph each solution

For $x \leq 12$

For $x \leq 20$

Step 4. Graph the numbers that make both inequalities true. x≤12 and x≤20

Step 5. Write the solution in interval notation.

$(- \infty, 12]$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{3}{4} (x - 8) \leq 3 a n d \frac{1}{5} (x - 5) \leq 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each solution

Step 4. Graph the numbers that make both inequalities true. x≤12 and x≤20

Step 5. Write the solution in interval notation.

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Solve each inequality, graph the solution, and write the solution in interval notation.34(x−8)≤3and15(x−5)≤3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each solution

Step 4. Graph the numbers that make both inequalities true. x≤12 and x≤20

Step 5. Write the solution in interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{3}{4} (x - 8) \leq 3 a n d \frac{1}{5} (x - 5) \leq 3$