Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point)
Responses
A. Division Property of Equality
B. Identity Property of Multiplication
C. Subtraction Property of Equality
D. Addition Property of Equality
C. Subtraction Property of Equality
To solve the equation "Five less than three-fourths of x is seven" when x equals 16, we need to find the value of x that satisfies the equation.
First, let's translate the sentence into an equation:
(3/4)x - 5 = 7
Next, we can simplify the equation by multiplying both sides by 4 to get rid of the fraction:
4[(3/4)x - 5] = 4 * 7
3x - 20 = 28
Now, let's isolate the variable x by adding 20 to both sides:
3x - 20 + 20 = 28 + 20
3x = 48
Finally, to solve for x, we divide both sides by 3:
(3x)/3 = 48/3
x = 16
Based on the steps taken, the last property of equality used to justify the solution to this problem is the Division Property of Equality. Therefore, the correct answer is: A. Division Property of Equality.