First slide

Theory of equations

Question

The number of solutions of $| x + 2 | = 2 (3 - x)$ is

Moderate

A

1
B

2
C

3
D

0

Solution

$2 (3 - x) = | x + 2 | \geq 0 \Rightarrow x \leq 3$
If $x \leq - 2$ , the equation becomes
$2 (3 - x) = - x - 2 \Rightarrow x = 8$ Not possible
If $- 2 < x \leq 3$ the equation becomes
$2 (3 - x) = x + 2 \Rightarrow 3 x = 4 \Rightarrow x = 4 / 3$

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