$$ \left. \begin{array} { c } { | 2.5 x - 6.8 | = 12.9 } \ { 2.5 x - 6.8 = - 12.9 \quad 2.5 x - 6.8 = 12.9 } \end{array} ight. $$

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$$ \left. \begin{array} { c } { | 2.5 x - 6.8 | = 12.9 } \ { 2.5 x - 6.8 = - 12.9 \quad 2.5 x - 6.8 = 12.9 } \end{array} ight. $$

UpStudy AI · Accepted Answer

Solve the equation $$ |2.5x - 6.8| = 12.9 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left|2.5x-6.8ight|=12.9$$
- step1: Simplify:
  $$\left|\frac{5}{2}x-\frac{34}{5}ight|=12.9$$
- step2: Calculate:
  $$\left|\frac{5}{2}x-\frac{34}{5}ight|=\frac{129}{10}$$
- step3: Separate into possible cases:
  $$\begin{align}&\frac{5}{2}x-\frac{34}{5}=\frac{129}{10}\&\frac{5}{2}x-\frac{34}{5}=-\frac{129}{10}\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=\frac{197}{25}\&x=-\frac{61}{25}\end{align}$$
- step5: Rewrite:
  $$x_{1}=-\frac{61}{25},x_{2}=\frac{197}{25}$$
The solutions to the equation $$|2.5x - 6.8| = 12.9$$ are $$x = -2.44$$ and $$x = 7.88$$.
The solutions are $$x = -2.44$$ and $$x = 7.88$$.

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