Chapter 2: Q 2.132 (page 193)

Solve The compound inequality. Graph the solution and write the solution in interval notation.
$\frac{3}{4} x - 3 \leq 3 o r \frac{2}{5} (x + 10) \geq 0$

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

Solve each Inequalities

$\frac{3}{4} x - 3 \leq 3 o r \frac{2}{5} (x + 10) \geq 0 \frac{3}{4} x - 3 + 3 \leq 3 + 3 \frac{5}{2} \times \frac{2}{5} (x + 10) \geq 0 \times \frac{5}{2} \frac{3}{4} x \leq 6 x + 10 \geq 0 \frac{3}{4} x \times \frac{4}{3} \leq 6 \times \frac{4}{3} x + 10 - 10 \geq 0 - 10 x \leq 8 x \geq - 10$

Graph the Solution

$G r a p h f o r \frac{3}{4} x - 3 \leq 3$

$G r a p h f o r \frac{2}{5} (x + 10) \geq 0$

By merging the above graphs we get it is true for all x

Solution and Interval Notation

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve The compound inequality. Graph the solution and write the solution in interval notation.
$\frac{3}{4} x - 3 \leq 3 o r \frac{2}{5} (x + 10) \geq 0$

Short Answer

Step by step solution

Solve each Inequalities

Graph the Solution

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

Statistics

Pure Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve The compound inequality. Graph the solution and write the solution in interval notation.34x-3≤3or25x+10≥0

Short Answer

Step by step solution

Solve each Inequalities

Graph the Solution

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

Statistics

Pure Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve The compound inequality. Graph the solution and write the solution in interval notation.
$\frac{3}{4} x - 3 \leq 3 o r \frac{2}{5} (x + 10) \geq 0$