Question

which of the following is(are) the solution(s) to $|5x + 2| = 8$?

a. $x = 2, -\frac{6}{5}$

b. $x = -2, \frac{6}{5}$

c. $x = \frac{6}{5}$

d. $x = 2$

Explanation:

Step1: Solve the absolute value equation

The equation is \(|5x + 2| = 8\). By the definition of absolute value, we have two cases:
Case 1: \(5x + 2 = 8\)
Subtract 2 from both sides: \(5x = 8 - 2 = 6\)
Divide both sides by 5: \(x=\frac{6}{5}\)
Case 2: \(5x + 2=-8\)
Subtract 2 from both sides: \(5x=-8 - 2=-10\)
Divide both sides by 5: \(x = - 2\)
So the solutions are \(x=-2,\frac{6}{5}\)

Answer:

B. \(x = -2,\frac{6}{5}\)