Question

Find the solution for the written expression the absolute value of the quantity negative 6 plus x end quantity is equal to zero.

a. x=6
b. x= no solution
c. x=-6
d. x=6 and -6

Answer 1

The solution to the expression |-6 + x| = 0 is x = 6, because the only way for an absolute value to equal zero is for the quantity inside to be zero. So the correct answer is Option A.

Step-by-step explanation:

The goal is to find the solution for the expression |-6 + x| = 0. The absolute value of a number is its distance from zero on a number line, which means it is always non-negative. For the absolute value of something to be equal to zero, the expression inside the absolute value must itself be zero. Thus, we can set up the equation without the absolute value:

-6 + x = 0

Adding 6 to both sides gives:

x = 6

Therefore, the solution to the equation |-6 + x| = 0 is x = 6. This is because the absolute value of zero is the only number that is zero, and if the quantity inside the absolute value is zero, the absolute value would indeed be zero.