Chapter 2: Q.380. (page 195)

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$5 x - 2 < 8 a n d 6 x + 9 \geq 3$

Short Answer

Expert verified

$T h e n u m b e r t h a t m a k e b o t h i n e q u a l i t i e s t r u e i s - 1 \leq x < 2 I n t e r v a l N o t a t i o n : [- 1, 2)$

Step by step solution

Step 1. Given information

$5 x - 2 < 8 a n d 6 x + 9 \geq 3$

Step 2. Solve Each Inequalities

$5 x - 2 < 8 \Rightarrow 5 x - 2 + 2 < 8 + 2 \Rightarrow 5 x < 10 \Rightarrow \frac{5 x}{5} < \frac{10}{5} \Rightarrow x < 2$ $6 x + 9 \geq 3 \Rightarrow 6 x + 9 - 9 \geq 3 - 9 \Rightarrow 6 x \geq - 6 \Rightarrow \frac{6 x}{6} \geq \frac{- 6}{6} \Rightarrow x \geq - 1$

Step 3. Graph each solution

Graph of $x < 2$

Graph of $x \geq - 1$

Step 4.Merge the graph of each solution

Step 5.Interval Notation

$T h e n u m b e r t h a t m a k e b o t h i n e q u a l i t i e s t r u e i s - 1 \leq x < 2 I n t e r v a l N o t a t i o n : [- 1, 2)$

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.

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$5 x - 2 < 8 a n d 6 x + 9 \geq 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve Each Inequalities

Step 3. Graph each solution

Step 4.Merge the graph of each solution

Step 5.Interval Notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.5x-2<8and6x+9≥3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve Each Inequalities

Step 3. Graph each solution

Step 4.Merge the graph of each solution

Step 5.Interval Notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$5 x - 2 < 8 a n d 6 x + 9 \geq 3$