Chapter 2: Q.2.131 (page 193)

Solve the compound inequality. Graph the solution and write the solution in interval notation. $\frac{3}{5} x - 7 \leq - 1 o r \frac{1}{3} (x + 6) \geq - 2$

Short Answer

Expert verified

$S o l u t i o n : T r u e f o r a l l x I n t e r v a l N o t a t i o n : (- \infty, \infty)$

Step by step solution

Step 1. Given information

$\frac{3}{5} x - 7 \leq - 1 o r \frac{1}{3} (x + 6) \geq - 2$

Step 2. Solve Each Inequalities

$\frac{3}{5} x - 7 \leq - 1 o r \frac{1}{3} (x + 6) \geq - 2 \frac{3}{5} x - 7 + 7 \leq - 1 + 7 \frac{1}{3} (x + 6) \times 3 \geq - 2 \times 3 \frac{3}{5} x \leq 6 x + 6 \geq - 6 \frac{3}{5} x \times \frac{5}{3} \leq 6 \times \frac{5}{3} x + 6 - 6 \geq - 6 - 6 x \leq 10 x \geq - 12$

Step 3. Graph Each Solution

Graph of $\frac{3}{5} x - 7 \leq - 1$

Graph of $\frac{1}{3} (x + 6) \geq - 2$

By Merging the above graphs of inequalities we get it is True for all x

Step 4. Solution and Interval Notation

$S o l u t i o n : T r u e f o r a l l x I n t e r v a l N o t a t i o n : (- \infty, \infty)$

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Solve the compound inequality. Graph the solution and write the solution in interval notation. $\frac{3}{5} x - 7 \leq - 1 o r \frac{1}{3} (x + 6) \geq - 2$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve Each Inequalities

Step 3. Graph Each Solution

Step 4. Solution and Interval Notation

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Solve the compound inequality. Graph the solution and write the solution in interval notation.35x-7≤-1or13x+6≥-2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve Each Inequalities

Step 3. Graph Each Solution

Step 4. Solution and Interval Notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the compound inequality. Graph the solution and write the solution in interval notation. $\frac{3}{5} x - 7 \leq - 1 o r \frac{1}{3} (x + 6) \geq - 2$