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Q. 8 PT

Expert-verifiedFound in: Page 325

Book edition
Student Edition

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

Pages
801 pages

ISBN
9780078884801

**Solve each inequality. Check your solution.**

**$\mathbf{3}\mathit{c}\mathbf{-}\mathbf{7}\mathbf{<}\mathbf{11}$**

The solution of the given inequality $3c-7<11$ is $\mathit{c}\mathbf{<}\mathbf{6}$.

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 $\frac{a}{c}>\frac{b}{c}$.

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

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

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

To perform the check of the solution, substitute a number less than 6 as $c<6$ in the given inequality $3c-7<11$, 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 $3c-7<11$.

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

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

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