Chapter 2: Q. 421 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$\frac{1}{5} (x - 5) + 6 < 4$ and $3 - \frac{2}{3} x < 5$

Short Answer

Expert verified

The solution of the inequality: $(- \infty, - 5)$ and $(- 3, \infty)$

Interval notation: $[- 5, - 3]$

The graph of the inequality on number line is

Step by step solution

Step 1. Given Information.

We have:

$\frac{1}{5} (x - 5) + 6 < 4$ and

$3 - \frac{2}{3} x < 5$

Step 2. Solve the inequality.

First, solve $\frac{1}{5} (x - 5) + 6 < 4$ :

Subtract $6$ from both sides:

$\frac{1}{5} (x - 5) + 6 - 6 < 4 - 6 \frac{1}{5} (x - 5) < - 2 5 \cdot \frac{1}{5} (x - 5) < 5 (- 2) x - 5 < - 10 x - 5 + 5 < - 10 + 5 x < - 5$

Internal notation: $(- \infty, - 5)$

Now, solve $3 - \frac{2}{3} x < 5 :$

Subtract $3$ from both sides:

$3 - \frac{2}{3} x - 3 < 5 - 3 - \frac{2}{3} x < 2$

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

$(- \frac{2}{3} x) (- 1) > 2 (- 1) \frac{2}{3} x > - 2 3 \cdot \frac{2}{3} x > 3 (- 2) 2 x > - 6 \frac{2 x}{2} > \frac{- 6}{2} x > - 3$

Interval notation: $(- 3, \infty)$

Step 3. Draw the solution on the number line.

Draw the solution $(- \infty, - 5)$ and $(- 3, + \infty)$ on the number line:

By combining the both solutions, we get:

$[- 5, - 3]$

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$\frac{1}{5} (x - 5) + 6 < 4$ and $3 - \frac{2}{3} x < 5$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on the number line.

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Solve the inequality, graph the solution on the number line, and write the solution in interval notation: 15x-5+6<4and 3-23x<5

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Solve the inequality.

Step 3. Draw the solution on the number line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Decision Maths

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Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:
$\frac{1}{5} (x - 5) + 6 < 4$ and $3 - \frac{2}{3} x < 5$