Amby02 wrote:

If |x + 1| = 2|x - 1|, what is the sum of the roots?

A. 4

B. 6

C. 8

D. 20/3

E. 10/3

The only way the two sides will be equal is if quantities inside the absolute value brackets are 1) equal or 2) equal but with opposite signs. |x| = y or -y*

1. Remove the brackets

2. LHS = RHS or LHS = -RHS*

3. Set up the two equations

CASE 1: x + 1 = 2(x - 1) OR

CASE 2: x + 1 = -[2(x -1)]

4. Solve

CASE 1:

x + 1 = 2x - 2

3 = x ... x = 3

CASE 2:

x + 1 = -[2(x -1)]

x + 1 = -(2x - 2)

x + 1 = -2x + 2

3x = 1

x = \(\frac{1}{3}\)

5. Check x = 3 and x = \(\frac{1}{3}\) When removing absolute value brackets, I always check to see whether or not the roots satisfy the original equation. Both work.

6. Sum of roots is 3 + \(\frac{1}{3}\) = \(\frac{10}{3}\)

Answer D

*(and |y| = x or -x). You can reverse RHS and LHS, where RHS = LHS or RHS = - LHS.

pushpitkc shows the four possibilities. The latter two are identical to the first two.

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