Question

Three less then 3 times a number is equal to 23 less than half the number.

(a) Translate the sentence into an equation.
(b) Solve the equation. Show your work.

Answer 1

Let x be a number. Then:

• 3 times a number is 3x;
• Three less then 3 times a number is 3-3x;
• half the number is $\dfrac{1}{2}x;$
• 23 less than half the number is $23-\dfrac{1}{2}x.$

(a) Thus, the equation is

$3-3x=23-\dfrac{1}{2}x.$

(b) Multiply this equation by 2:

$6-6x=46-x,\\\\-6x+x=46-6,\\\\-5x=40,\\\\5x=-40,\\\\x=-8.$