Question

4.07 Homework (due 1/8/21) Directions: Solve the following inequalities. SHOW ALL STEPS LEARNED IN CLASS WHERE APPLICABLE. 1. I 1-8x - 31 > 11 2. 1x + 5 - 6

Answer 1

1.

`|-8x-3|>1`

we separate the inequality into two parts to solve the absolute value

`\begin{gathered} -8x-3>1 \\ \& \\ -8x-3<-1 \end{gathered}`

first part

`\begin{gathered} -8x-3>1 \\ -3-1>8x \\ -(4)/(8)>x \\ \\ x<-(1)/(2) \end{gathered}`

second part

`\begin{gathered} -8x-3<-1 \\ -3+1<8x \\ -(2)/(8)-(1)/(4) \end{gathered}`

graph

where the yellow lines are the first part, red the second part and the solution of the inequality is the union of these two

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

2.

`\begin{gathered} |x+5|-6<-5 \\ |x+5|<1 \end{gathered}`

we separate the inequality into two parts to solve the absolute value

`\begin{gathered} x+5<1 \\ \& \\ x+5>-1 \end{gathered}`

first part

`\begin{gathered} x+5<1 \\ x<1-5 \\ x<-4 \end{gathered}`

second part

`\begin{gathered} x+5>-1 \\ x>-1-5 \\ x>-6 \end{gathered}`

graph

where the first part is yellow, the second part is red and the solution of the inequality is green

`-4>x>-6`