Question

Twelve more than the product of a number and 2 is less than -5. Find the number.

• A. $x<-\frac{17}{2}$
• B. $x<-\frac{17}{2}$
• C. $x>-\frac{17}{2}$
• D. $x\le -\frac{17}{2}$

Answer 1

The correct option is A $x<-\frac{17}{2}$

Let the unknown number be $x$.
Given,
The product of a number and 2 $=x\times 2$
Twelve more than the product of a number $=2x+12$
Twelve more than the product of a number and 2 is less than -5:
$\Rightarrow 2x+12<-5$

Subtract 12 from both sides of the inequality
$\Rightarrow 2x+12-12<-5-12$
$\Rightarrow 2x<-17$

Divide by 2 on both sides of the inequality
$\Rightarrow \frac{2x}{2}<-\frac{17}{2}$
$\Rightarrow x<-\frac{17}{2}$

It can be represented on the numberline as:
A opened circle at $-\frac{17}{2}$ and the red line goes to the right, indicating that $x$ is less than $-\frac{17}{2}$.