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Question

# Solve the inequality. Graph and check the solution.$55>-7 v+6$

Solution

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Step 1
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Subtract $6$ from the both sides.

\begin{align*} 55-6&> -7v+6-6\\ 49&> -7v&&\text{Divide both sides by}\,\, (-7).\\ \dfrac{\cancel{7}\cdot 7}{(-\cancel{7})}&< \dfrac{\cancel{(-7)}\cdot v}{\cancel{(-7)}}&&\text{Reverse the direction of inequality, due to the division with a negative number}\\ -7&

Check the solution for $v>-7$. For example, ${\color{#c34632}v=-6}$.

\begin{align*} 55\mathop>\limits^{?}-7\cdot(-6)+6\\ 55\mathop>\limits^{?}42+6\\ 55\mathop>\limits^{?}48\\ True\\ \end{align*}

This inequality is shown in the picture.

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