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The movement of the progress bar may be uneven because Solve for $$ x: 4|2 x-5|+6=10 $$

UpStudy AI · Accepted Answer

Solve the equation $$ 4|2x-5|+6=10 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4\left|2x-5ight|+6=10$$
- step1: Move the expression to the left side:
  $$4\left|2x-5ight|+6-10=0$$
- step2: Subtract the numbers:
  $$4\left|2x-5ight|-4=0$$
- step3: Separate into possible cases:
  $$\begin{align}&4\left(2x-5ight)-4=0,2x-5\geq 0\&4\left(-\left(2x-5ight)ight)-4=0,2x-5<0\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=3,x\geq \frac{5}{2}\&x=2,x<\frac{5}{2}\end{align}$$
- step5: Find the intersection:
  $$\begin{align}&x=3\&x=2\end{align}$$
- step6: Rewrite:
  $$x_{1}=2,x_{2}=3$$
The solutions to the equation $$4|2x-5|+6=10$$ are $$x=2$$ and $$x=3$$.
The solutions are $$ x=2 $$ and $$ x=3 $$.

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