Chapter 2: Q.389. (page 195)

In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$

Short Answer

Expert verified

Solution:- $x \geq 2$

Interval:- $[- 2, \infty)$

The solution graph is

Step by step solution

Step 1.Given information

$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$

Step 2.Solve Each Inequalities

$- 3 (x + 4) < 0 \Rightarrow 3 (x + 4) > 0 \Rightarrow (x + 4) > 0 \Rightarrow x > - 4 a n d - 1 (3 x - 1) \leq 7 \Rightarrow (3 x - 1) \geq - 7 \Rightarrow 3 x \geq - 7 + 1 \Rightarrow 3 x \geq - 6 \Rightarrow x \geq - 2$

Step 3. Graph of each solution

Graph of $- 3 (x + 4) < 0$

Graph of $- 1 (3 x - 1) \leq 7$

Step 4. Merge Overlapping intervals

Step 5.Interval notation

$[- 2, \infty)$

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In the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities

Step 3. Graph of each solution

Step 4. Merge Overlapping intervals

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.−3(x+4)<0and−1(3x−1)≤7

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities

Step 3. Graph of each solution

Step 4. Merge Overlapping intervals

Step 5.Interval notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Mechanics Maths

Statistics

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.
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$