Q3. Absolute Value

Question

If |3r - 5| = 10 and |r + 2| = 7, then what is the value of r?

a) 5

b) 3

c) -3

d) -5

Explanation

1st equation

|3r - 5| = 10

3r - 5 = 10 or 3r - 5 = -10

r = 5 or r = -3.

For the other equation

|r + 2| = 7

r + 2 = 7 or r + 2 = -7

r = 5 or r = -9

Only r = 5 (option A) satisfies both equations.

Lesson

The absolute value of a negative number always has a positive value.

When working an absolute value problem such as the one above, note that there are two possible solutions for each equation after taking out the absolute value sign, one where the inside is positive and one where the inside is negative.

Want more practice questions? Check out the Worthington Prep SAT Tutoring Questions page.