Question

1. three times a number, decreased by 14, is the same as 22 decreased by five times the number. find the number.

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

"Three times a number, decreased by 14" can be written as \( 3x - 14 \).
"22 decreased by five times the number" can be written as \( 22 - 5x \).
Since they are the same, the equation is \( 3x - 14 = 22 - 5x \).

Step3: Solve the equation for \( x \)

Add \( 5x \) to both sides: \( 3x + 5x - 14 = 22 - 5x + 5x \), which simplifies to \( 8x - 14 = 22 \).
Add 14 to both sides: \( 8x - 14 + 14 = 22 + 14 \), which simplifies to \( 8x = 36 \).
Divide both sides by 8: \( x = \frac{36}{8} = \frac{9}{2} = 4.5 \).

Answer:

The number is \( \frac{9}{2} \) (or 4.5).