Question

Write the solution set and its representation on the number line for the following inequation.
$\frac{x+1}{3}<15-7x\le -3(x-7);x\in R.$

• A. $-1.5\le x<2$
  
• B. $-1.5<x<3$
  
• C. $-1.5<x<2$
  
• D. $-1.5\le x\le 2$
  

Answer 1

The correct option is A

$-1.5\le x<2$

Given: $\frac{x+1}{3}<15-7x\le -3(x-7)$

Let's separate the given inequation in two inequation.

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the below inequations.

$\begin{array}{c}-3(x-7)\ge 15-7x\\ -3x+21\ge 15-7x\\ 4x\ge -6\\ x\ge \frac{-6}{4}\\ x\ge -1.5\end{array}|\begin{array}{c}15-7x>\frac{x+1}{3}\\ 15-\frac{1}{3}>\frac{x}{3}+7x\\ \frac{45-1}{3}>\frac{x+21x}{3}\\ 44>22x\\ 2>x\end{array}$

The solution can be represented on the number line as shown below.




Hence, $-1.5\le x<2$.