Question

Solve for x: |4x - 2| < 8.

OPTION 1: x < 2
OPTION 2: x > 2
OPTION 3: x < 10/4
OPTION 4: x > 10/4

Answer 1

The solution to |4x - 2| < 8 is x > -1.5 and x < 2.5. The closest option provided is Option 3: x < 10/4, as this represents x < 2.5.

Step-by-step explanation:

To solve the inequality |4x - 2| < 8, we must consider two cases due to the absolute value.

1. First, if the expression inside the absolute value is positive, the equation becomes 4x - 2 < 8. Adding 2 to both sides gives 4x < 10, which simplifies to x < 2.5.
2. Second, if the expression inside the absolute value is negative, we must reverse the inequality sign, giving us -(4x - 2) < 8. This simplifies to -4x + 2 < 8. When we subtract 2 from both sides, we get -4x < 6, and dividing by -4 (and reversing the inequality sign since we are dividing by a negative number) gives us x > -1.5.

Combined, these inequalities yield a solution set of -1.5 < x < 2.5.

Thus, the correct options from the list provided by the student would be:

• Option 3: x < 10/4 because 10/4 is 2.5
• There is no option given for x > -1.5, but it would be an essential part of the full solution.