Question

Solve the equation. Check the solutions.

$|5x+9|+6=1$

Short answer

No solution for $x\in \mathrm{ℝ}$.

Step-by-step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line,without considering direction. The absolute value of a number is never negative.

Step 2- Simplify the expression.

Consider the expression $|5x+9|+6=1$.

Subtract 6 from both sides of the equation as follows:

$\begin{array}{l}|5x+9|+6=1\\ |5x+9|+6-6=1-6\\ |5x+9|=-5\end{array}$

Step 3- Step description.

There is no value of x that makes the equation true because an absolute value can never be negative.

Therefore, no solution for $x\in \mathrm{ℝ}$