Question

problem #7: if 3 times a number is increased by 22, the result is 14 less than 7 times the number. what is the number? what are you trying to find out: workspace: solution:

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

"3 times a number is increased by 22" can be written as \( 3x + 22 \). "14 less than 7 times the number" can be written as \( 7x - 14 \). So the equation is \( 3x + 22 = 7x - 14 \).

Step3: Solve the equation for \( x \)

Subtract \( 3x \) from both sides: \( 22 = 4x - 14 \).
Add 14 to both sides: \( 36 = 4x \).
Divide both sides by 4: \( x = 9 \).

Answer:

The number is 9.