Chapter 2: Q. 422 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$4 x - 2 > 6$ or
$3 x - 1 \leq - 2$

Short Answer

Expert verified

The solution of the inequality: $x > 2$ or $x \leq - \frac{1}{3}$

Interval notation: localid="1644836093627" role="math" $(- \infty, - \frac{1}{3}] \cup (2, + \infty)$

The graph of the inequality on number line is:

Step by step solution

Step 1. Given Information.

We have:

$4 x - 2 > 6$ or

$3 x - 1 \leq - 2$

Step 2. Solve the inequality

First. solve $4 x - 2 > 6$ :

Add $2$ from both sides:

$4 x - 2 + 2 > 6 + 2 4 x > 8 \frac{4 x}{4} > \frac{8}{4} x > 2$

Interval notation: $(2, \infty)$

Now, solve $3 x - 1 \leq - 2 :$

Add $1$ to both sides:

$3 x - 1 + 1 \leq - 2 + 1 3 x \leq - 1 \frac{3 x}{3} \leq \frac{- 1}{3} x \leq - \frac{1}{3}$

Interval notation: $(- \infty, - \frac{1}{3}]$

Step 3. Draw the solution on number line.

Now, draw the solution $x > 2$ or $x \leq - \frac{1}{3}$ :

By combining both the inequalities, we get:

$(- \infty, - \frac{1}{3}] \cup (2, + \infty)$

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$4 x - 2 > 6$ or
$3 x - 1 \leq - 2$

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:4x-2>6or3x-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

Geometry

Calculus

Statistics

Mechanics Maths

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$4 x - 2 > 6$ or
$3 x - 1 \leq - 2$