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

`-(2)/(5)x-9<(9)/(10)`

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

`\begin{gathered} -(2)/(5)x-9+9<(9)/(10)+9 \\ -(2)/(5)x<(9)/(10)+(90)/(10) \\ -(2)/(5)x<(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} -(2)/(5)x\cdot(-1)<(99)/(10)\cdot(-1) \\ (2)/(5)x>-(99)/(10) \end{gathered}`

Multiplying both sides by 5, we have

`\begin{gathered} (2)/(5)x\cdot5>-(99)/(10)\cdot5 \\ 2x>-(99)/(2) \end{gathered}`

And finally, dividing both sides by 2

`\begin{gathered} 2x\cdot(1)/(2)>-(99)/(2)\cdot(1)/(2) \\ x>-(99)/(4) \end{gathered}`