Chapter 2: Q.388. (page 195)

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$3 (2 x - 3) > 3 a n d 4 (x + 5) \geq 4$

Short Answer

Expert verified

The number that make both Inequalities true is x > 2

Interval Notation: ( 2, ∞ )

The solution graph is

Step by step solution

Step 1.Given information

$3 (2 x - 3) > 3 a n d 4 (x + 5) \geq 4$

Step 2.Solve Each Inequalities

$3 (2 x - 3) > 3 \Rightarrow \frac{3 (2 x - 3)}{3} > \frac{3}{3} \Rightarrow 2 x - 3 > 1 \Rightarrow 2 x - 3 + 3 > 1 + 3 \Rightarrow 2 x > 4 \Rightarrow \frac{2 x}{2} > \frac{4}{2} \Rightarrow x > 2 4 (x + 5) \geq 4 \Rightarrow \frac{4 (x + 5)}{4} \geq \frac{4}{4} \Rightarrow x + 5 \geq 1 \Rightarrow x + 5 - 5 \geq 1 - 5 \Rightarrow x \geq - 4$

Step 3. Draw the graph

Graph of $3 (2 x - 3) > 3$

Graph of $4 (x + 5) \geq 4$

Merged both solution

Step 4.Interval Notation

The number that make both Inequalities true is x > 2

Interval Notation: ( 2, ∞ )

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In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$3 (2 x - 3) > 3 a n d 4 (x + 5) \geq 4$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities

Step 3. Draw the graph

Step 4.Interval Notation

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In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.3(2x-3)>3and4(x+5)≥4

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities

Step 3. Draw the graph

Step 4.Interval Notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Probability and Statistics

Calculus

Geometry

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.
$3 (2 x - 3) > 3 a n d 4 (x + 5) \geq 4$