Question

8x + 8 > -64 and -7 - 8x>-79

Answer 1

In order to find the solution of this system of inequations, let's isolate the variable x in each inequation:

`\begin{gathered} 8x+8>-64 \\ 8x>-64-8 \\ 8x>-72 \\ x>-(72)/(8) \\ x>-9 \\ \\ -7-8x>-79 \\ -8x>-79+7 \\ -8x>-72 \\ 8x<72 \\ x<(72)/(8) \\ x<9 \end{gathered}`

We have that x > -9 and x < 9, so the solution is the interval -9 < x < 9.

Other notations for this answer are:

[tex]\begin{gathered} \text{set-builder notation: }\mleft\lbrace x\mright|-9