Question

Solve the inequality $2x-5\le \frac{(4x-7)}{3}$

• A. $x\in (-\infty ,4)$
• B. $x\in (-\infty ,4]$
• C. $x\in (-\infty ,8]$
• D. $x\in (-\infty ,-4]$

Answer 1

The correct option is B

$x\in (-\infty ,4]$

Explanation for the correct option:

Given:

$2x-5\le \frac{(4x-7)}{3}$

Multiply $3$ on both sides

$$\begin{gathered} \Rightarrow 3\left(2x-5\right)\le (4x-7) \\ \Rightarrow 6x-15\le (4x-7) \end{gathered}$$

On Simplifying we get

$$\begin{gathered} \Rightarrow 6x-4x\le 15-7 \\ \Rightarrow 2x\le 8 \\ \Rightarrow x\le \frac{8}{2} \\ \Rightarrow x\le 4 \end{gathered}$$

Therefore, $x\in (-\infty ,4]$

Hence, option (B) is the correct answer.