Question

What is the solution set for this inequality? 5x − 4 < 11 + 8x

Answer 1

Answer: x>-5

Explanation:

add 4 to both sides

5x-4+4<11+8x+4

simplify

5x<8x+15

subtract 8x from both sides

5x-8x<8x+15

simplify

-3x<15

divide both sides by -3 and switch inequality sign

-3x/-3>-15/-3

x>-5

Answer 2

`\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 11+8x \end{gathered}$}`

Simplify both sides of the inequality.

`\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 8x+11 \end{gathered}$}`

Subtract 8x from both sides.

`\large\displaystyle\text{$\begin{gathered}\sf 5x-4-8x < 8x+11-8x \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf -3x-4 < 11 \end{gathered}$}`

Add 4 to both sides.

`\large\displaystyle\text{$\begin{gathered}\sf -3x-4+4 < 11+4 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf -3x < 15 \end{gathered}$}`

Divide both sides by -3.

`\large\displaystyle\text{$\begin{gathered}\sf (-3x)/(-3) < (15)/(-3) \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf x > -5 \ \ \iff \ \ \ Answer \end{gathered}$}`

{ Pisces04 }