Chapter 2: Q. 410 (page 195)

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{3}{4} x - 2 > 4 o r 4 (2 - x) > 0$

Short Answer

Expert verified

Solution of inequalities

$x > 8 o r x < 2$

Graph of solution of inequalities

The solution in interval notation.

$(- \infty, 2) \cup (8, \infty)$

Step by step solution

Step 1. Given information

Consider the inequality

$\frac{3}{4} x - 2 > 4 o r 4 (2 - x) > 0$

Step 2. Solve each inequality

$\frac{3}{4} x - 2 > 4 \frac{3}{4} x > 4 + 2 \frac{3}{4} x > 6 x > 6 \times \frac{4}{3} x > 8$ or $4 (2 - x) > 0 2 - x > \frac{0}{4} 2 - x > 0 - x > - 2 x < 2$

Step 3. Graph each inequality

For $x > 8$

For $x < 2$

Step 4. Graph number that make either one inequality true x>8 or x<2

The solution in interval notation

$(- \infty . 2) \cup (8, \infty)$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{3}{4} x - 2 > 4 o r 4 (2 - x) > 0$

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>8 or x<2

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Solve each inequality, graph the solution, and write the solution in interval notation. 34x−2>4or4(2−x)>0

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>8 or x<2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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.
$\frac{3}{4} x - 2 > 4 o r 4 (2 - x) > 0$