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

x = 3

Step-by-step explanation

Given inequality:

`(x+5)/(3)<2x`

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

`\begin{gathered} (x+5)/(3)*3<2x*3 \\ =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} (-5x)/(-5)>(-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}`