Chapter 2: Q316 (page 183)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$12 x + 3 (x + 7) > 10 x - 24$

Short Answer

Expert verified

$x > - 9$

$(- 9, \infty)$

Step by step solution

Step 1. Given information.

The following inequality is given:

$12 x + 3 (x + 7) > 10 x - 24$

Step 2. Solving the inequality.

Distributing and combining like terms

$12 x + 3 x + 21 > 10 x - 24 15 x + 21 > 10 x - 24$

Subtracting $10 x + 21$ from both sides and simplifying

$15 x + 21 - 10 x - 21 > 10 x - 24 - 10 x - 21 5 x > - 45 x > \frac{- 45}{5} x > - 9$

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below

Step 4. Writing the solution in the interval notation.

In the interval notation, the solution can be written as

$(- 9, \infty)$

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.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$12 x + 3 (x + 7) > 10 x - 24$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.12x+3x+7>10x-24

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line.

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$12 x + 3 (x + 7) > 10 x - 24$