Chapter 2: Q. 655 (page 299)

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$3 c - 10 (c - 2) < 5 c + 16$ .

Short Answer

Expert verified

The solution for the given inequality is, $c > \frac{1}{3}$ .

A graph for the solution on the number line is,

From the number line, the obtained interval notation is, $(\frac{1}{3}, \infty)$ .

Step by step solution

Step 1. Given information

$3 c - 10 (c - 2) < 5 c + 16$ .

Step 2. First solve the given inequality.

Simplify each side as much as possible by using the distributive property.

$3 c - 10 (c - 2) < 5 c + 16 3 c - 10 c + 20 < 5 c + 16 - 7 c + 20 < 5 c + 16$

Add $7 c$ on both the sides of the equation to collect the variable on the right side and then simplify it.

$- 7 c + 7 c + 20 < 5 c + 7 c + 16 20 < 12 c + 16$

Step 3. Now subtract 16 on the both sides of the equation to collect the constants on the left side and then simplify it.

$20 - 16 < 12 c + 16 - 16 4 < 12 c \frac{4}{12} < c c > \frac{1}{3}$

Step 4. Now graph the solution on the number line.

Write the solution in the interval notation.

From the number line, the obtained interval notation is, $(\frac{1}{3}, \infty)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$3 c - 10 (c - 2) < 5 c + 16$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. First solve the given inequality.

Step 3. Now subtract 16 on the both sides of the equation to collect the constants on the left side and then simplify it.

Step 4. Now graph the solution on the number line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.3c−10(c−2)<5c+16.

Short Answer

Step by step solution

Step 1. Given information

Step 2. First solve the given inequality.

Step 3. Now subtract 16 on the both sides of the equation to collect the constants on the left side and then simplify it.

Step 4. Now graph the solution on the number line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$3 c - 10 (c - 2) < 5 c + 16$ .