Solve the absolute value equation or indicate that the equation has no solution.

Question

Solve the absolute value equation or indicate that the equation has no solution. $$ |9 x+8|=|x-3| $$

UpStudy AI · Accepted Answer

Solve the equation $$ |9x+8|=|x-3| $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left|9x+8ight|=\left|x-3ight|$$
- step1: Evaluate:
  $$\begin{align}&9x+8=x-3\&9x+8=-\left(x-3ight)\end{align}$$
- step2: Calculate:
  $$\begin{align}&x=-\frac{11}{8}\&x=-\frac{1}{2}\end{align}$$
- step3: Rewrite:
  $$x_{1}=-\frac{11}{8},x_{2}=-\frac{1}{2}$$
The absolute value equation $$|9x+8|=|x-3|$$ has two solutions: $$x=-\frac{11}{8}$$ and $$x=-\frac{1}{2}$$.
The solutions are $$ x=-\frac{11}{8} $$ and $$ x=-\frac{1}{2} $$.

Solve the absolute value equation or indicate that the equation has no solution.

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