Question

Solve the inequality 2e+6(e+3)<2e+8, and write the solution in interval notation.

Answer 1

Given the inequality

$2e+6(e+3)<2e+8$

Step 1: Remove the bracket using distributive property and simplify

$\begin{gathered} 2e+6(e)+6(3)<2e+8 \\ 2e+6e+18<2e+8 \end{gathered}$

Step 2: Collect like terms and simplfy to find the set of values for e

$\begin{gathered} 2e+6e-2e<8-18 \\ 8e-2e<-10 \\ 6e<-10(\text{divide both sides by 6)} \\ \frac{6e}{6}<\frac{-10}{6} \\ e<-\frac{5}{3} \end{gathered}$

Step 3: Write the inequality solution in interval notation

[tex]\begin{gathered} e<-\frac{5}{3}\Rightarrow-\infty