Question

consider the following problem.
the difference between five times a number and 7 is equal to three times the sum of the number and 5. find the number.
if x represents the number, which equation is correct for solving this problem?
...
choose the correct answer below.
a. $5x - 7 = 3x + 5$
b. $5x - 7 = 3(x + 5)$
c. $7 - 5x = 3(x + 5)$
d. $7 - 5x = 3x + 5$

Explanation:

Step1: Analyze "five times a number"

Let the number be \( x \), five times the number is \( 5x \).

Step2: Analyze "the difference between five times a number and 7"

The difference between \( 5x \) and 7 is \( 5x - 7 \) (since it's "five times a number" minus 7, as the wording is "difference between five times a number and 7", which is \( 5x - 7 \) not \( 7 - 5x \) as the number is multiplied by 5 first and then we take the difference with 7).

Step3: Analyze "three times the sum of the number and 5"

The sum of the number (\( x \)) and 5 is \( x + 5 \), and three times that sum is \( 3(x + 5) \).

Step4: Set up the equation

Since the two expressions are equal, the equation is \( 5x - 7 = 3(x + 5) \).

Answer:

B. \( 5x - 7 = 3(x + 5) \)