Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q21.

Expert-verified

Algebra 1

Found in: Page 302

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Solve each inequality. Check your solution.
$2 x + 11 \leq 5 x - 10$

The required value of x is $[7, \infty)$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\leq or \geq$ , use the bracket or a solid circle at that endpoint.

Properties of inequality:

$1. b \leq c \Rightarrow b \pm a \leq c \pm a \begin{array}{l} 2. b \leq c \Rightarrow a b \leq a c, if a > 0 \\ 3. b \leq c \Rightarrow a b \geq a c, if a < 0 \end{array}$

Step 2. Solve the inequality for x.

In order to solve the inequality:

$2 x + 11 \leq 5 x - 10$

Subtract both sides of the inequality by 2x, as

$\begin{matrix} 2 x + 11 \leq 5 x - 10 \\ 2 x + 11 - 2 x \leq 5 x - 10 - 2 x \\ 11 \leq 3 x - 10 \\ 11 + 10 \leq 3 x - 10 + 10 \\ 21 \leq 3 x \\ \frac{21}{3} \leq \frac{3 x}{3} \\ 7 \leq x \\ x \geq 7 \end{matrix}$

Thus, the inequality is true for x greater than or equal to 7, thus the solution of given inequality in interval form is, as $[7, \infty)$ .

Step 3. Check the solution.

To check the answer solution for the given inequality.

First check the solution at end point by converting it into an equation.

If the solution is less than m, then pick any value of x less than m and check whether it satisfies the inequality.

If the solution is greater than m, then pick any value of x greater than m and check whether it satisfies the inequality.

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting x equals to 7 in the inequality as

$\begin{matrix} 2 (7) + 11 \leq 5 (7) - 10 \\ 25 \leq 25 \\ Left Hand side = Right Hand side \end{matrix}$

Now put any value any value of x greater than 7, say 9 and check whether it satisfies the inequality, as

$\begin{matrix} 2 (9) + 11 \leq 5 (9) - 10 \\ 18 + 11 \leq 45 - 10 \end{matrix} 29 \leq 35 [True]$

Since, both conditions are satisfied thus solution of inequality is correct.

Most popular questions for Math Textbooks

Solve each inequality. Check your solution.

$- 9 m < - 36$

Define a variable, write an inequality, and solve the problem. Check your solution. The difference of a number and 4 is no more than 8.

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of an inequality of the form $y < a x + b$ is a region on the coordinate plane called a half-plane.

Sanjay has $$ 65$ to spend at the mall. He bought a T-shirt for $$ 18$ and a belt for $$ 14$ . If Sanjay wants a pair of jeans, how much can he spend?

Graph the solution set for the inequality $3 x - 6 \leq 4 x - 4 \leq 3 x + 1$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free