Q41. - Algebra 1

Question

Solve each equation. Then graph the solution set.

$4-3\left|q\right|=10$

Step-by-Step Solution

Answer

The equation $4-3\left|q\right|=10$ has solution set as $q=-2,2$ and the graph of the solution set is:

Step-1. Define absolute value equation.

For any real numbers a and b, if $\left|a\right|=b$ and $b\ge 0$, then $a=b$ or $a=-b$.

Step-2. Formulate case 1 when 4 − 3 q = 10 .

Simplify the expression for q.

$\begin{array}{c}4-3q-4=10-4\\ -3q=6\\ \frac{-3q}{3}=\frac{6}{3}\\ -q\times \left(-1\right)=2\times \left(-1\right)\\ q=-2\end{array}$

Step-3. Formulate case 2 when 4 − 3 − q = 10 .

Simplify the expression for q.

$\begin{array}{c}4-3\left(-q\right)-4=10-4\\ 3q=6\\ \frac{3q}{3}=\frac{6}{3}\\ q=2\end{array}$

Step-4. Plot the graph of the solution set.

From case 1 and case 2, $q=-2,2$. Plot these values on the number line.