Chapter 2: Q. 411 (page 195)

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{2}{3} x - 3 > 5 o r 3 (5 - x) > 6$

Short Answer

Expert verified

Solution of inequalities

$x < 3 o r x > 12$

Graph of solution of inequalities

The solution in interval notation.

$(- \infty, 3) \cup (12, \infty)$

Step by step solution

Step 1. Given information

Consider the inequality

$\frac{2}{3} x - 3 > 5 o r 3 (5 - x) > 6$

Step 2. Solve each inequality

$\frac{2}{3} x - 3 > 5 \frac{2}{3} x > 5 + 3 \frac{2}{3} x > 8 x > 8 \times \frac{3}{2} x > 12$ or $3 (5 - x) > 6 5 - x > \frac{6}{3} 5 - x > 2 - x > 2 - 5 - x > - 3 x < 3$

Step 3. Graph each inequality

For $x < 3$

For $x > 12$

Step 4. Graph number that make either one inequality true x<3 or x >12

The solution in interval notation

$(- \infty, 3) \cup (12, \infty)$

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Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{2}{3} x - 3 > 5 o r 3 (5 - x) > 6$

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<3 or x >12

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Solve each inequality, graph the solution, and write the solution in interval notation.23x−3>5or3(5−x)>6

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<3 or x >12

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Applied Mathematics

Mechanics Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each inequality, graph the solution, and write the solution in interval notation.
$\frac{2}{3} x - 3 > 5 o r 3 (5 - x) > 6$