Question

Solve each equation. Then graph the solution set.

$\left|\frac{1}{2}x+5\right|=-3$

Short answer

The equation$\left|\frac{1}{2}x+5\right|=-3$ has empty solution set as $\varphi$.

Step-by-step solution

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. Observe the equation.

In the given equation, $\left|\frac{1}{2}x+5\right|=-3$, the distance between $\frac{1}{2}x$and $5$ is negative, that is., $-3$, which is not possible as distance can never be negative.

Step-3. State the conclusion.

Since, distance is a non-negative quantity therefore, no value of x would satisfy the equation.

Hence, the solution set will be an empty set for the given equation.