Chapter 2: Q.389. (page 195)

Solve compound Inequalities with "and"
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$

Short Answer

Expert verified

The number that make both Inequalities true is x ≥ - 2

Interval Notation: [-2, ∞ )

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 and Draw Graph

$- 3 (x + 4) < 0 \Rightarrow \frac{- 3 (x + 4)}{- 3} > \frac{0}{- 3} (W h e n w e M u l t i p l y o r d i v i d e b y n e g a t i v e n u m b e r, i n e q u a l i t i e s c h a n g e s) \Rightarrow x + 4 > 0 \Rightarrow x + 4 - 4 > 0 - 4 \Rightarrow x > - 4$

$- 1 (3 x - 1) \leq 7 \Rightarrow \frac{- 1 (3 x - 1)}{- 1} \geq \frac{7}{- 1} \Rightarrow 3 x - 1 \geq - 7 \Rightarrow 3 x - 1 + 1 \geq - 7 + 1 \Rightarrow 3 x \geq - 6 \Rightarrow \frac{3 x}{3} \geq \frac{- 6}{3} \Rightarrow x \geq - 2$

Step 3.Graph of each solution

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

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

Merging both graph

Step 4. Interval Notation

The number that make both Inequalities true is x ≥ - 2

Interval Notation: [-2, ∞ )

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Solve compound Inequalities with "and"
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities and Draw Graph

Step 3.Graph of each solution

Step 4. Interval Notation

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Solve compound Inequalities with "and"-3(x+4)<0and-1(3x-1)≤7

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve Each Inequalities and Draw Graph

Step 3.Graph of each solution

Step 4. Interval Notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Solve compound Inequalities with "and"
$- 3 (x + 4) < 0 a n d - 1 (3 x - 1) \leq 7$