What is the answer to |a+1|-6=1 ?

The answer to |a+1|-6=1 is a=-8\lor a=6

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|a+1|-6=1

∣ a + 1 ∣ - 6 = 1

a = - 8 or a = 6

Solution steps

∣ a + 1 ∣ - 6 = 1

Move

6

to the right side

∣ a + 1 ∣ = 7

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

a + 1 = - 7 or a + 1 = 7

a + 1 = - 7 or a + 1 = 7

a = - 8 or a = 6

∣ x ∣ = x^{3} + 2 x^{2} - 3 x

∣ x + 3 ∣ = 2 x + 4

2 ∣ x + 1 ∣ - ∣ 2 x - 4 ∣ = 1

∣ x + 1 ∣ + ∣ 5 x - 2 ∣ = 6

(x - 3)^{2} - 12 ∣ x - 3 ∣ + 35 = 0