Solve for x: \(|x + 2| + 16 = 14\)

1. \(x = -32\) and \(x = -4\)
2. \(x = -4\) and \(x = 0\)
3. \(x = 0\) and \(x = 28\)
4. No solution

(x+2) + 16 = 14 -16] [-16 x+2 = -2 -2] [-2 x = -4
so the logical option is option 2, but you should put your numbers back into the original equation to check they're right.
when x = -4 (x+2) +16 = (-4 +2) +16 = -2 + 16 = 14 which is correct
when x = 0 (x+2) + 16 = (0+2) + 16 = 2 + 16 = 18 which is incorrect
and since we worked out x and know that none of the other numerical options are possible, I would say option 4 (no solution) is the answer.
Hope this helped.

Answered by CatInThePark | 2024-06-10

∣ x + 2∣ + 16 = 14 ∣ s u b t r a c t 16 ∣ x + 2∣ = − 2 x + 2 = − 2 or − x − 2 = − 2 x = − 4 or − x = 0 x = − 4 or x = 0

Answered by luana | 2024-06-10

The equation ∣ x + 2∣ + 16 = 14 leads to no solution because the absolute value cannot equal a negative number. Thus, the correct choice is option 4: No solution.
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Answered by CatInThePark | 2024-12-26