Chapter 2: Q. 415 (page 196)

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

Short Answer

Expert verified

Solution of inequalities

$x \leq - 4 o r x \geq - 14$

Graph of solution of inequalities

The solution in interval notation

$(- \infty, \infty)$

Step by step solution

Step 1. Given information

Consider each inequality

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

Step 2. Solve each inequality

$\frac{3}{4} x + 2 \leq - 1 \frac{3}{4} x \leq - 1 - 2 \frac{3}{4} x \leq - 3 x \leq - 3 \times \frac{4}{3} x \leq - 4$ or $\frac{1}{2} (x + 8) \geq - 3 x + 8 \geq - 3 \times 2 x + 8 \geq - 6 x \geq - 6 - 8 x \geq - 14$

Step 3. Graph each inequality

For $x \leq - 4$

For $x \geq - 14$

Step 4. Graph number that make either one inequality true x≤-4 or x≥-14

The solution in interval notation

$(- \infty, - 4] \cup [- 14, \infty) = (- \infty, \infty)$

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

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≤-4 or x≥-14

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Solve each inequality, graph the solution, and write the solution in interval notation. 34x+2≤−1or12(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≤-4 or x≥-14

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Calculus

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

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