Question

Consider the following statements
Statement I The solution set of $2\le 3x-4\le 5$ is $(2,3)$
Statement II $(-80,-10)$ is the solution set of $-12<4-\frac{3x}{-5}\le 2$
Choose the correct option.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (D)

I. The given inequality $2\le 3x-4\le 5$
$\Rightarrow 2+4\le 3x\le 5+4$
$\Rightarrow 6\le 3x\le 9$
Dividing by 3 in each term,
$\frac{6}{3}\le \frac{3x}{3}\le \frac{9}{3}$
$\Rightarrow 2\le x\le 3$
$\therefore$ Solution set is $[2,3]$.
II. The given inequality
$-12<4-\frac{3x}{-5}\le 2$
$\Rightarrow -12<4+\frac{3x}{5}\le 2$
Adding $(-4)$ to each term,
$-12-4<4+\frac{3x}{5}-4\le 2-4$
$\Rightarrow -16<\frac{3x}{5}\le -2$
Multiplying by $\frac{5}{3}$ to each term,
$-16\times \frac{5}{3}<\frac{3x}{5}\times \frac{5}{3}\le -2\times \frac{5}{3}$
$\Rightarrow -\frac{80}{3}<x\le -\frac{10}{3}$
$\therefore \text{ Solution set is }\left(-\frac{80}{3},-\frac{10}{3}\right]\text{ or }]-\frac{80}{3},\frac{-10}{3}]$