Carcass wrote:
\(3 |x - 4| = 16\)
Quantity A |
Quantity B |
\(x\) |
\(\frac{28}{3}\) |
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says:
If |x| = k, then x = k and/or x = -k2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
GIVEN: 3|x - 4| = 16
Divide both sides by 3 to get: |x - 4| = 16/3
Based on the above rule, we get TWO possible equations:
x - 4 = 16/3 and
x - 4 = -16/3 Let's solve each equation...
Take:
x - 4 = 16/3Add 4 to both sides to get: x = 16/3 + 4
Rewrite with common denominator: x = 16/3 + 12/3
Combine fractions to get: x = 28/3
In this case, the two quantities are EQUAL
Take:
x - 4 = -16/3Add 4 to both sides to get: x = -16/3 + 4
Rewrite with common denominator: x = -16/3 + 12/3
Combine fractions to get: x = -4/3
In this case, the two Quantity B IS GREATER
Answer: D
_________________
Brent Hanneson - founder of Greenlight Test Prep