Question

select the correct answer. the difference of a number and 6 is the same as 5 times the sum of the number and 2. what is the number? a. -4 b. -2 c. -1 d. 1

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

The difference of the number and 6 is \( x - 6 \), and 5 times the sum of the number and 2 is \( 5(x + 2) \). Since they are the same, we have the equation:
\( x - 6 = 5(x + 2) \)

Step3: Solve the equation

First, expand the right side:
\( x - 6 = 5x + 10 \)

Then, subtract \( x \) from both sides:
\( -6 = 4x + 10 \)

Next, subtract 10 from both sides:
\( -16 = 4x \)

Finally, divide both sides by 4:
\( x = -4 \)

Answer:

A. -4