Question

1. determine the solutions of the equation |8x + 10| - 6 = 0

a. no real solution
b. 2 and 0.5
c. - 2 and - 0.5
d. - 0.5

Explanation:

Step1: Isolate the absolute value

Start with the equation \(|8x + 10| - 6 = 0\). Add 6 to both sides to isolate the absolute value:
\(|8x + 10| = 6\)

Step2: Set up two cases

The absolute value equation \(|A| = B\) (where \(B \geq 0\)) is equivalent to \(A = B\) or \(A = -B\). Here, \(A = 8x + 10\) and \(B = 6\) (which is non - negative), so we have two cases:

• Case 1: \(8x+10 = 6\)

Subtract 10 from both sides: \(8x=6 - 10=-4\)
Divide both sides by 8: \(x=\frac{-4}{8}=-0.5\)

• Case 2: \(8x + 10=-6\)

Subtract 10 from both sides: \(8x=-6 - 10=-16\)
Divide both sides by 8: \(x=\frac{-16}{8}=-2\)

Answer:

c. \(-2\) and \(-0.5\)