Chapter 2: Q. 390 (page 195)

Solve each inequality, graph the
solution, and write the solution in interval notation.
$\frac{1}{2} (3 x - 4) \leq 1 a n d \frac{1}{3} (x + 6) \leq 4$

Short Answer

Expert verified

Solution of each inequalities:

$x \leq 2 a n d x \leq 6$

Graph the numbers that make both inequalities true:

Solution in interval notation:

$(- \infty, 2]$

Step by step solution

Step 1. Given information

Consider the inequalities

$\frac{1}{2} (3 x - 4) \leq 1 a n d \frac{1}{3} (x + 6) \leq 4$

Step 2. Solve each inequality

$\frac{1}{2} (3 x - 4) \leq 1 3 x - 4 \leq 1 \times 2 3 x - 4 \leq 2 3 x \leq 2 + 4 3 x \leq 6 x \leq \frac{6}{3} x \leq 2$ and $\frac{1}{3} (x + 6) \leq 4 x + 6 \leq 4 \times 3 x + 6 \leq 12 x \leq 12 - 6 x \leq 6$

Step 3. Graph each solution of inequality

For $x \leq 2$

For $x \leq 6$

Step 4. Graph the numbers that make both inequalities true.x≤2 and x≤6

Step 5. Write the solution in interval notation.

$(- \infty, 2]$

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Solve each inequality, graph the
solution, and write the solution in interval notation.
$\frac{1}{2} (3 x - 4) \leq 1 a n d \frac{1}{3} (x + 6) \leq 4$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each solution of inequality

Step 4. Graph the numbers that make both inequalities true.x≤2 and x≤6

Step 5. Write the solution in interval notation.

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Solve each inequality, graph thesolution, and write the solution in interval notation.12(3x−4)≤1and13(x+6)≤4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each solution of inequality

Step 4. Graph the numbers that make both inequalities true.x≤2 and x≤6

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

Applied Mathematics

Logic and Functions

Calculus

Pure Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the
solution, and write the solution in interval notation.
$\frac{1}{2} (3 x - 4) \leq 1 a n d \frac{1}{3} (x + 6) \leq 4$