$$ 1 \leftarrow \begin{array}{l}\begin{array}{l} ext { Solve the equation. Then determine whether the equ } \ ext { equation. }\end{array} \ \qquad \begin{array}{l}\frac{x+7}{2}-8=\frac{2 x-6}{3}\end{array} \ ext { What is the solution? Select the correct choice below }\end{array} $$

Question

$$ 1 \leftarrow \begin{array}{l}\begin{array}{l}	ext { Solve the equation. Then determine whether the equ } \ 	ext { equation. }\end{array} \ \qquad \begin{array}{l}\frac{x+7}{2}-8=\frac{2 x-6}{3}\end{array} \ 	ext { What is the solution? Select the correct choice below }\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{x+7}{2}-8=\frac{2x-6}{3} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x+7}{2}-8=\frac{2x-6}{3}$$
- step1: Multiply both sides of the equation by LCD:
  $$\left(\frac{x+7}{2}-8ight)	imes 6=\frac{2x-6}{3}	imes 6$$
- step2: Simplify the equation:
  $$3x-27=4x-12$$
- step3: Move the expression to the left side:
  $$3x-4x=-12+27$$
- step4: Add and subtract:
  $$-x=-12+27$$
- step5: Add and subtract:
  $$-x=15$$
- step6: Change the signs:
  $$x=-15$$
The solution to the equation $$ \frac{x+7}{2}-8=\frac{2x-6}{3} $$ is $$ x = -15 $$.
The solution is $$ x = -15 $$.

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