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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

User Silverburgh
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1.


|-8x-3|>1

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


\begin{gathered} -8x-3>1 \\ \&amp; \\ -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 \\ \&amp; \\ 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

4.07 Homework (due 1/8/21) Directions: Solve the following inequalities. SHOW ALL-example-1
4.07 Homework (due 1/8/21) Directions: Solve the following inequalities. SHOW ALL-example-2
User Heslacher
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