Question

The sum of a number and 81 is greater than the product of -3 and that number. What are the possible values of the number?

• A. $x>-20\frac{1}{4}$
• B. $x<-22\frac{1}{4}$
• C. $x>-23\frac{1}{4}$
• D. $x>-21\frac{1}{4}$

Answer 1

The correct option is A $x>-20\frac{1}{4}$

Let the number be x.
From the condition, we have:
$x+81>-3x$
$x+81-81>-3x-81$ (subtracting 81 from both the sides)
$x>-3x-81$
$x+3x>-3x-81+3x$ (adding 3x on both the sides)
$4x>-81$
$\frac{4x}{4}>-\frac{81}{4}$
$x>-20\frac{1}{4}$
The number is greater than $-20\frac{1}{4}$.