Question

what are the solutions of this equation? |5x + 10| - 15 = 0
a. 1 and -1
b. 1 and -5
c. 5 and -5
d. -1 and 5

Explanation:

Step1: Isolate the absolute value

Start with the equation \(|5x + 10| - 15 = 0\). Add 15 to both sides to isolate the absolute value:
\(|5x + 10| = 15\)

Step2: Set up two cases

The absolute value equation \(|A| = B\) (where \(B \geq 0\)) splits into \(A = B\) or \(A = -B\). Here, \(A = 5x + 10\) and \(B = 15\), so:
Case 1: \(5x + 10 = 15\)
Case 2: \(5x + 10 = -15\)

Step3: Solve Case 1

Subtract 10 from both sides: \(5x = 15 - 10 = 5\)
Divide by 5: \(x = \frac{5}{5} = 1\)

Step4: Solve Case 2

Subtract 10 from both sides: \(5x = -15 - 10 = -25\)
Divide by 5: \(x = \frac{-25}{5} = -5\)

Answer:

B. 1 and -5