arpitjain 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
So, if |x + 3| = 4x, we get:
x + 3 = 4x and
x + 3 = -4xLet's solve each equation.
Take:
x + 3 = 4x Subtract x from both sides:
3 = 3x Solve:
x = 1Plug
x = 1 into original equation to get: |
1 + 3| = 4(
1)
Simplify: 4 = 4. Works!!
So,
x = 1 is a VALID solution
----------------------------------
Take:
x + 3 = -4x Subtract x from both sides:
3 = -5x Solve:
x = -3/5 Plug
x = -3/5 into original equation to get: |
-3/5 + 3| = 4(
-3/5)
Simplify: 12/15 = -12/15. DOESN'T WORK
So,
x = -3/5 is NOT a valid solution
----------------------------------------
Since
x = 1 is the ONLY valid solution, we get:
QUANTITY A:
1QUANTITY B: 1
Answer: C
Cheers,
Brent