Half the sum of a number, x, and 15 is at most the sum of the opposite of twice the number and 1.25. What is the range of possible values for the number?

1 Answer
May 7, 2018

Any value smaller than -2.5 (included) is fine: the range is

R = {x \in \mathbb{R}: x \leq -2.5}

Explanation:

If you know that A is at most B, it means that A can't be more than B, and thus is lesser or equal to B. So, we will have something like A \leq B.

Let's translate A and B:

A:

  • The sum of a number x and 15 \implies x+15
  • Half the sum of a number x and 15 \implies \frac{x+15}{2}

B:

  • The opposite of the number implies -x
  • The opposite of twice the number \implies -2x
  • The sum of the opposite of twice the number and 1.25 \implies -2x+1.25

So, we have

\frac{x+15}{2} \leq -2x+1.25

Multiply both sides by two:

x+15 \leq -4x+2.5

Bring all the x terms of the left and the numbers to the right:

5x \leq -12.5

Solve for x:

x \leq -\frac{12.5}{5} = -2.5