list $$ 1 \leftarrow \begin{array}{r} ext { Solve and check the equation } \ \frac{8 x}{9}=\frac{x}{2}+7 \ 14\end{array} $$

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list $$ 1 \leftarrow \begin{array}{r}	ext { Solve and check the equation } \ \frac{8 x}{9}=\frac{x}{2}+7 \ 14\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{8x}{9}=\frac{x}{2}+7 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{8x}{9}=\frac{x}{2}+7$$
- step1: Multiply both sides of the equation by LCD:
  $$\frac{8x}{9}	imes 18=\left(\frac{x}{2}+7ight)	imes 18$$
- step2: Simplify the equation:
  $$16x=9x+126$$
- step3: Move the variable to the left side:
  $$16x-9x=126$$
- step4: Subtract the terms:
  $$7x=126$$
- step5: Divide both sides:
  $$\frac{7x}{7}=\frac{126}{7}$$
- step6: Divide the numbers:
  $$x=18$$
The solution to the equation $$ \frac{8x}{9}=\frac{x}{2}+7 $$ is $$ x=18 $$.
$$ x=18 $$

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