Question

Kuta Software Infinite Algebra 2 Compound Inequalities Solve each compound inequality and graph 1) nis-3 or -4n 11 ntlezon ine-8 -3tis int3Ln-84-40 L+1-3 - na 8 -32 hotez - 4-86 -80-33!! and sa -8a31143 -80>14 17) 9m - 8 3) 2 < 2x < 6

Answer 1

That is absolute value.

$|x|\text{ = +x or -x}$$\begin{gathered} |-8a\text{ - 3| > 11} \\ (-8a\text{ - 3) > 11 or -(-8a - 3) > 11} \\ (-8a\text{ - 3) > 11} \\ -8a\text{ > 11 + 3} \\ -8a\text{ > 14} \\ a\text{ < }\frac{-14}{8} \\ a\text{ < }\frac{-7}{2} \end{gathered}$

or

$\begin{gathered} -(-8a\text{ - 3) > 11} \\ 8a\text{ + 3 > 11} \\ 8a\text{ > 11 - 3} \\ 8a\text{ > 8} \\ a\text{ > 8/8} \\ a\text{ > 1} \end{gathered}$

Therefore,

1 < a <-7/2