Question

Solve the equation $\left|2x+7\right|+5=0$.

Short answer

The given equation hasno real solution.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $\left|2x+7\right|+5=0$.

Step 2. Simplify the equation.

The given equation $\left|2x+7\right|+5=0$is solved as:

$\begin{array}{l}\left|2x+7\right|+5=0\mathrm{....}\left(\text{Given}\right)\\ \left|2x+7\right|+5+\left(-5\right)=0+\left(-5\right)\mathrm{....}\left(\begin{array}{l}\text{Add}-5\\ \text{bothsides}\end{array}\right)\\ \left|2x+7\right|=-5\end{array}$

Now, $\left|2x+7\right|=-5$ gives $x\notin R$ (real).

Hence there is no real solution for the given equation.

Step 3. Conclusion.

The given equation has no real solution.