Study Guides | inequalities | Inequalities with Multiplication and Division

Study Guide: Inequalities with Multiplication and Division

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Example

\begin{align} -18 &\lt 6t &\textit{Original} \\[3ex] \frac{-18}{6} &\lt \frac{6t}{6} &\textit{Inverse operation} \\[3ex] -3 &\lt t &\textit{Solution} \\[3ex] t &\gt -3 &\textit{Rewrite with the variable on left.} \\\ & &\textit{Remember to flip the inequality symbol!} \end{align}

Exercises

Solve each inequality and graph the solution.

  1. $3a \le 15$
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  1. $\frac{p}{4} \gt 2$
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  1. $-3n \lt -18 $
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  1. $-2k \lt 14$
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  1. $27 \lt -9h$
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  1. Euphemia is starting a new art project. She wants to decorate some notebooks to give away during the Winter Holidays. What are the possible numbers of notebooks costing $1.39 that can be purchased with $10?
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  1. $a \le 5$

  2. $p \gt 8$

  3. $n \gt 6$

  4. $k \gt -7$

  5. $ h \lt -3$

  6. Let $n$ equal the possible number of notebooks that can be purchased for $10 or less.

\begin{align} n &\le \frac{\$10.00}{\$1.39} &\textit{Original inequality} \\[3ex] n &\le 7.19 &\textit{n must be a whole number less than 7.19}\\[3ex] n &= \{ 0, 1, 2, 3, 4, 5, 6, 7 \} &\textit{Solution Set}\\[3ex] \end{align}

Source: https://class.ronliskey.com/study/mathematics-8/8-3-3-inequalities-with-mult-and-div/