# Determine whether the given problem is an equation or an expression. If it is an

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. $$\displaystyle\frac{{{2}{x}+{7}}}{{8}}+{x}-{2}=\frac{{{x}-{1}}}{{2}}$$

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Usamah Prosser

Step 1
Given:
$$\displaystyle{\frac{{{2}{x}+{7}}}{{{8}}}}+{x}-{2}={\frac{{{x}-{1}}}{{{2}}}}$$
It contains signs therefore it is an equation.
$$\displaystyle\Rightarrow{\frac{{{2}{x}+{7}}}{{{8}}}}+{x}-{2}={\frac{{{x}-{1}}}{{{2}}}}$$
multiply by 8 we get,
$$2x+7+8x−16=4(x−1)$$
$$10x−9=4x−4$$
$$6x=9−4$$
$$6x=5$$
$$\displaystyle{x}={\frac{{{5}}}{{{6}}}}$$
Step 2
Therefore,
$$\displaystyle{x}={\frac{{{5}}}{{{6}}}}$$