Q19. - Algebra 1

Question

Solve each inequality. Check your solution.

$\frac{1}{5}g\ge -4$

Step-by-Step Solution

Answer

The solution of the given inequality $\frac{1}{5}g\ge -4$ is $g\ge -20$.

Check:

 

To perform the check of the solution, substitute a number greater than or equal to $-20$ as $g\ge -20$ in the given inequality $\frac{1}{5}g\ge -4$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $g=0$, as $0\ge -20$.

Now substitute 0 for in the inequality $\frac{1}{5}g\ge -4$.

$$\begin{gathered} \frac{1}{5}g\ge -4 \\ \frac{1}{5}\left(0\right)\ge -4 \\ 0\ge -4 \end{gathered}$$

As, the condition obtained $0\ge -4$ is true, therefore the solution is correct.

Step 1. Write the multiplication property of inequalities.

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

(i) If $a>b$ and c is a positive number then $ac>bc$.

(ii) If $a<b$ and c is a positive number then $ac<bc$.

(ii) If $a>b$ and c is a negative number then $ac<bc$.

(iv) If $a<b$ and c is a negative number then width="53" style="max-width: none; vertical-align: -5px;" $ac>bc$.

Step 2. Solve the given inequality 1 5 g &#8805; &#8722; 4 .

The solution of the given inequality $\frac{1}{5}g\ge -4$ is:

$$\begin{gathered} \frac{1}{5}g\ge -4 \\ \left(5\right)\left(\frac{1}{5}g\right)\ge \left(5\right)\left(-4\right)\left(\text{by using mutiplication property of inequality}\right) \\ g\ge -20 \end{gathered}$$

Therefore, the solution of the given inequality $\frac{1}{5}g\ge -4$ is $g\ge -20$.

Step 3. Check the solution.

To perform the check of the solution, substitute a number greater than or equal to $-20$ as $g\ge -20$ in the given inequality $\frac{1}{5}g\ge -4$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $g=0$, as $0\ge -20$.

Now substitute 0 for g in the inequality $\frac{1}{5}g\ge -4$.

$$\begin{gathered} \frac{1}{5}g\ge -4 \\ \frac{1}{5}\left(0\right)\ge -4 \\ 0\ge -4 \end{gathered}$$

As, the condition obtained $0\ge -4$ is true, therefore the solution is correct.