Question

If $x$ satisfies the inequations $2x-7<11\text{and}3x+4<-5$, then $x$ lies in the interval

• A. $\left(-\infty ,3\right)$
• B. $\left(-\infty ,2\right)$
• C. $\left(-\infty ,-3\right)$
• D. $\left(-\infty ,\infty \right)$
• E. $\left(3,\infty \right)$

Answer 1

The correct option is C

$\left(-\infty ,-3\right)$

Explanation for the correct option.

Step 1: Solve $2x-7<11$

$\begin{array}{rcl}2x-7& <& 11\\ \Rightarrow 2x& <& 18\\ \Rightarrow x& <& 9\end{array}$

Step 2: Solve $3x+4<-5$

$\begin{array}{rcl}3x+4& <& -5\\ \Rightarrow 3x& <& -9\\ \Rightarrow x& <& -3\end{array}$

Therefore, $x$ lies in the interval $\left(-\infty ,-3\right)$.

Hence, option C is correct.