Chapter 2: Q.381. (page 195)

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$4 x - 1 < 7 a n d 2 x + 8 \geq 4$

Short Answer

Expert verified

The Graph of Each Solution

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

Step by step solution

Step 1. Given information

$4 x - 1 < 7 a n d 2 x + 8 \geq 4$

Step 2. Solve Each Inequalities

$4 x - 1 < 7 \Rightarrow 4 x - 1 + 1 < 7 + 1 \Rightarrow 4 x < 8 \Rightarrow \frac{4 x}{4} < \frac{8}{4} \Rightarrow x < 2$ $2 x + 8 \geq 4 \Rightarrow 2 x + 8 - 8 \geq 4 - 8 \Rightarrow 2 x \geq - 4 \Rightarrow \frac{2 x}{2} \geq \frac{- 4}{2} \Rightarrow x \geq - 2$

Step 3.Graph Each Solution

Graph of $4 x - 1 < 7$

Graph of $2 x + 8 \geq 4$

Step 4.Merge The Graph of Each Solution

Step 5.Interval Notation

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

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In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$4 x - 1 < 7 a n d 2 x + 8 \geq 4$

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

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In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.4x-1<7and2x+8≥4

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

Probability and Statistics

Mechanics Maths

Pure Maths

Discrete Mathematics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$4 x - 1 < 7 a n d 2 x + 8 \geq 4$