Question

What are the solutions of the inequality? Check the solutions. -2/5x - 9 < 9/10

Answer 1

We want to find the solutions for the following inequality

$-\frac{2}{5}x-9<\frac{9}{10}$

First, we can add 9 on both sides of the inequality

$\begin{gathered} -\frac{2}{5}x-9+9<\frac{9}{10}+9 \\ -\frac{2}{5}x<\frac{9}{10}+\frac{90}{10} \\ -\frac{2}{5}x<\frac{99}{10} \end{gathered}$

Now, we can multiply both sides by (-1). When we multiply an inequality by a negative number, it changes the sign

$\begin{gathered} -\frac{2}{5}x\cdot(-1)<\frac{99}{10}\cdot(-1) \\ \frac{2}{5}x>-\frac{99}{10} \end{gathered}$

Multiplying both sides by 5, we have

$\begin{gathered} \frac{2}{5}x\cdot5>-\frac{99}{10}\cdot5 \\ 2x>-\frac{99}{2} \end{gathered}$

And finally, dividing both sides by 2

$\begin{gathered} 2x\cdot\frac{1}{2}>-\frac{99}{2}\cdot\frac{1}{2} \\ x>-\frac{99}{4} \end{gathered}$