Question

Solve each equation. Then graph the solution set.

|2a + 1| = 1

a. a = 1
b. a = 0
c. a = -1
d. a = -0.5

Answer 1

The absolute value equation |2a + 1| = 1 has two solutions: a = 0 and a = -1. The graph of the solution set is represented by closed circles at these two points on the number line.

Step-by-step explanation:

Solving Absolute Value Equations

To solve the equation |2a + 1| = 1, we must consider two cases due to the property of absolute value:

1. When the quantity inside the absolute value is non-negative, i.e., 2a + 1 = 1. Solving for a we subtract 1 from both sides to get 2a = 0, and dividing both sides by 2 gives us a = 0.
2. When the quantity inside the absolute value is negative, i.e., 2a + 1 = -1. Solving for a, we subtract 1 from both sides to get 2a = -2, and then we divide both sides by 2 to find a = -1.

The solution set is {-1, 0}. To graph the solution set on a number line, we place closed circles on -1 and 0 because these are the values where the equation is true.

Checking the provided options, the correct answers are (b) a = 0 and (c) a = -1.