Asmakan wrote:
\(|x+3|=4x\)
Quantity A |
Quantity B |
x |
1 |
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says:
If |x| = k, then x = k or x = -k2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots
Given: |x + 3| = 4x
So, according to the above algorithm, EITHER x + 3 = 4x OR x + 3 = -4x
Let's examine each case...
Case i: x + 3 = 4x
Solve to get: x = 1
Plug x = 1 back into the original equation to get: |1 + 3| = 4(1)
Simplify both sides to get: |4| = 4.
WORKS!So, x = 1 is a valid solution
Case ii: x + 3 = -4x
Solve to get: x = -3/5
Plug x = -3/5 back into the original equation to get: |-3/5 + 3| = 4(-3/5)
Simplify both sides to get: |2 2/5| = -12/5.
DOESN'T WORKSo, x = -3/5 is not a valid solution
So the ONLY valid solution is x = 1
We get:
QUANTITY A: 1
QUANTITY B: 1
Answer: C
Cheers,
Brent