Chapter 2: Q. 424 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 2 (3 x - 4) \leq 2$ and
$- 4 (x - 1) < 2$

Short Answer

Expert verified

The solution of the inequality: $x \geq 1$ and $x > \frac{1}{2}$

Interval notation: $[1, \infty)$

The graph of the inequality on number line is:

Step by step solution

Step 1. Given Information.

We have:

$- 2 (3 x - 4) \leq 2$ and

$- 4 (x - 1) < 2$

Step 2. Solve the inequality.

First, solve $- 2 (3 x - 4) \leq 2$ :

Multiply both sides by $- 1$ (reverse the inequality):

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

Now, solve $- 4 (x - 1) < 2$ :

Multiply both sides by $- 1$ (reverse the inequality):

$(- 4 (x - 1)) (- 1) > 2 (- 1) 4 (x - 1) > - 2 \frac{4 (x - 1)}{4} > \frac{- 2}{4} x - 1 > - \frac{1}{2} x - 1 + 1 > - \frac{1}{2} + 1 x > \frac{1}{2}$

Step 3. Draw the solution on number line.

Now, draw the solution $x \geq 1$ and $x > \frac{1}{2}$ on the number line:

By combining both the inequalities, we get:

Interval notation: $[1, \infty)$

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 2 (3 x - 4) \leq 2$ and
$- 4 (x - 1) < 2$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on number line.

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation: -23x-4≤2and-4x-1< 2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on number line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$- 2 (3 x - 4) \leq 2$ and
$- 4 (x - 1) < 2$