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Q. 8 PT

Expert-verified

Algebra 1

Found in: Page 325

Book edition Student Edition

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

Pages 801 pages

ISBN 9780078884801

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Short Answer

Solve each inequality. Check your solution.
$3 c - 7 < 11$

The solution of the given inequality $3 c - 7 < 11$ is $c < 6$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the addition and division property of inequalities.

The addition property of inequalities states that if the same number is added to each side of a true inequality, the resulting inequality is also true that is:

If $a > b$ , then $a + c > b + c$ .
If $a < b$ , then $a + c < b + c$ .

The division property of inequalities states that if both sides of the inequality are divided by a positive number the sign of the inequality remains the same and if both sides of the inequality are divided by a negative number then the sign of the inequality changes that is:

If $a > b$ and $c$ is a positive number then $\frac{a}{c} > \frac{b}{c}$ .
If $a < b$ and $c$ is a positive number then $\frac{a}{c} < \frac{b}{c}$ .
If $a > b$ and $c$ is a negative number then $\frac{a}{c} < \frac{b}{c}$ .
If $a < b$ and $c$ is a negative number then $\frac{a}{c} > \frac{b}{c}$ .

Step 2. Solve the given inequality 3c−7<11.

The solution of the given inequality $3 c - 7 < 11$ is:

$\begin{matrix} 3 c - 7 < 11 \\ 3 c - 7 + 7 < 11 + 7 (by using addition property of inequality) \\ 3 c < 18 \\ \frac{3 c}{3} < \frac{18}{3} (by using division property of inequality) \\ c < 6 \end{matrix}$

Therefore, the solution of the given inequality $3 c - 7 < 11$ is $c < 6$ .

Step 3. Check the solution.

To perform the check of the solution, substitute a number less than 6 as $c < 6$ in the given inequality $3 c - 7 < 11$ , if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $c = 5$ , as $5 < 6$ .

Now substitute 5 for $c$ in the inequality $3 c - 7 < 11$ .

$\begin{matrix} 3 c - 7 < 11 \\ 3 (5) - 7 < 11 \\ 15 - 7 < 11 \\ 8 < 11 \end{matrix}$

As, the condition obtained $8 < 11$ is true, therefore the solution is correct.

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