Solve these equations algebraically |1/2 𝑥 − 3| = −5

Answer 1

To solve the equation algebraically |1/2 𝑥 − 3| = -5, we need to consider two cases.

Case 1: 1/2 𝑥 − 3 is positive

Since the absolute value expression is equal to -5, which is negative, there is no solution for this case. (A positive number cannot be equal to a negative number.)

Case 2: 1/2 𝑥 − 3 is negative

In this case, we can remove the absolute value brackets and negate the expression inside, giving us:

1/2 𝑥 − 3 = -(-5)

Simplifying, we have:

1/2 𝑥 − 3 = 5

Add 3 to both sides:

1/2 𝑥 = 8

Multiply both sides by 2:

𝑥 = 16

Therefore, the solution to the equation |1/2 𝑥 − 3| = -5 is 𝑥 = 16.