Chapter 2: Q. 419 (page 196)

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{1}{2} x - 5 \leq 3 o r \frac{1}{4} (x - 8) \geq - 3$

Short Answer

Expert verified

Solution of inequalities

$x \leq 16 o r x \geq - 4$

Graph of solution of inequalities

The solution in interval notation

$(- \infty, \infty)$

Step by step solution

Step 1. Given information

Consider each inequality

$\frac{1}{2} x - 5 \leq 3 o r \frac{1}{4} (x - 8) \geq - 3$

Step 2. Solve each inequality

$\frac{1}{2} x - 5 \leq 3 \frac{1}{2} x \leq 3 + 5 \frac{1}{2} x \leq 8 x \leq 8 \times 2 x \leq 16$ or $\frac{1}{4} (x - 8) \geq - 3 x - 8 \geq - 3 \times 4 x - 8 \geq - 12 x \geq - 12 + 8 x \geq - 4$

Step 3. Graph each inequality

For $x \leq 16$

For $x \geq - 4$

Step 4. Graph number that make either one inequality true x≤16 or x≥-4

The solution in interval notation

$(- \infty, 16] \cup [- 4, \infty) = (- \infty, \infty)$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{1}{2} x - 5 \leq 3 o r \frac{1}{4} (x - 8) \geq - 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each inequality

Step 4. Graph number that make either one inequality true x≤16 or x≥-4

One App. One Place for Learning.

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Solve each inequality, graph the solution, and write the solution in interval notation. 12x−5≤3or14(x−8)≥−3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve each inequality

Step 3. Graph each inequality

Step 4. Graph number that make either one inequality true x≤16 or x≥-4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{1}{2} x - 5 \leq 3 o r \frac{1}{4} (x - 8) \geq - 3$