Q. 5 PT - Algebra 1

Question

Solve each inequality. Check your solution.

$\mathbf{7}\mathit{w}\mathbf{\le }\mathbf{-}\mathbf{42}$

Step-by-Step Solution

Answer

The solution of the given inequality $7w\le -42$ is $\mathit{w}\mathbf{\le }\mathbf{-}\mathbf{6}$.

Step 1. Write the division property of inequalities.

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:

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

Step 2. Solve the given inequality 7 w &#8804; &#8722; 42 .

The solution of the given inequality $7w\le -42$ is:

$\begin{array}{c}7w\le -42\\ \frac{7w}{7}\le \frac{-42}{7}\left(\text{by using division property of inequality}\right)\\ w\le -6\end{array}$

Therefore, the solution of the given inequality $7w\le -42$ is $w\le -6$.

Step 3. Check the solution.

To perform the check of the solution, substitute a number less than or equal to $-6$ as $w\le -6$ in the given inequality $7w\le -42$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $w=-7$, as $-7\le -6$.

Now substitute $-7$ for $w$ in the inequality $7w\le -42$.

$\begin{array}{c}7w\le -42\\ 7\left(-7\right)\le -42\\ -49\le -42\end{array}$ 

As, the condition obtained $-49\le -42$ is true, therefore the solution is correct.