What is the answer to -6=8|2r+7|-6 ?

The answer to -6=8|2r+7|-6 is r=-7/2

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-6=8|2r+7|-6

- 6 = 8 ∣ 2 r + 7 ∣ - 6

r = - \frac{7}{2}

Decimal

r = - 3.5

Solution steps

- 6 = 8 ∣ 2 r + 7 ∣ - 6

Add

6

to both sides

- 6 + 6 = 8 ∣ 2 r + 7 ∣ - 6 + 6

Simplify

0 = 8 ∣ 2 r + 7 ∣

Switch sides

8 ∣ 2 r + 7 ∣ = 0

Divide both sides by

8

∣ 2 r + 7 ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

2 r + 7 = 0

2 r + 7 = 0 : r = - \frac{7}{2}

r = - \frac{7}{2}

∣ x + 9 ∣ = ∣ 6 - 2 x ∣

∣ p + 5 ∣ = 2

3 - \frac{1}{2} ∣ r + 9 ∣ = - 11

∣ x - 5 ∣ + 8 = 6

∣ x - 1 ∣ = ∣ 2 x ∣