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

melodykap 2021-10-01 Answered

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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Expert Answer

Usamah Prosser
Answered 2021-10-02 Author has 18125 answers

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,
\(\displaystyle{x}={\frac{{{5}}}{{{6}}}}\)

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