Question

Which of the following values is a solution to the inequality (x+5)/3 < 2x?Question 2 options:x = –5x = 13x = –1x = 3

Answer 1

Answer

x = 3

Explanation

Given inequality:

$\frac{x+5}{3}<2x$

Multiply both sides of the inequality by 3 in order to clear fraction:

$\begin{gathered} \frac{x+5}{3}\times3<2x\times3 \\ =x+5<6x \end{gathered}$

Combine the like terms

$\begin{gathered} x+5<6x \\ x-6x<-5 \\ -5x<-5 \end{gathered}$

Divide both sides by -5. Note the < will change to >

$\begin{gathered} \frac{-5x}{-5}>\frac{-5}{-5} \\ x>1 \end{gathered}$

This implies the values of x must be greater than 1, i.e. in terms of whole number, x = 2, x = 3, x = 4, ......... could be any of the solutions.

Hence,

$x=3\text{ is a solution to the inequality}$