A lot of students can get Absolute Value questions wrong. Ensuring you get this question right will help you gain 1-2 points. Absolute value always shows up on the ACT® Math Test, but only once or twice.
Absolute value means you solve within the absolute value bars first, then make whatever you get positive. Students think that absolute value means you need to convert everything to positives first. That's not entirely true. You need to evaluate the expression first, then make everything positive.
Consider these examples:
- |1 + 2| = 3
- |-1 + 2| = 1
- |1 - 2| = 1
How will this show up on the ACT® Math Test?
Absolute value tends to show up in 2 ways. The Test either wants you to solve basic problems with absolute value, as above. Or the test could ask you to find the positive and negative values for an equation.
|1x - 4| = 5 turns into…
1x - 4 = 5 or 1x - 4 = -5
Solving these gives x = 9 or x = -1.
The take away here is that x has both a positive and a negative value. That's because x could be either positive or negative in this context.
Practice Section
Question:
Solve for x: |2x + 3| = 7
- x = 2 or x = -5
- x = 5 or x = -2
- x = 2 or x = 5
- x = -2 or x = -5
Click for the Answer
Correct Answer: B. x = 5 or x = -2
Explanation:
To solve this, we set up two equations:
2x + 3 = 7 and 2x + 3 = -7
Solving these, we get:
x = 2 and x = -5
Therefore, the solution is x = 2 or x = -5.