What is the answer to 5|7w+1|+9=9 ?

The answer to 5|7w+1|+9=9 is w=-1/7

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5|7w+1|+9=9

5 ∣ 7 w + 1 ∣ + 9 = 9

w = - \frac{1}{7}

Decimal

w = - 0.14285 \dots

Solution steps

5 ∣ 7 w + 1 ∣ + 9 = 9

Subtract

9

from both sides

5 ∣ 7 w + 1 ∣ + 9 - 9 = 9 - 9

Simplify

5 ∣ 7 w + 1 ∣ = 0

Divide both sides by

5

∣ 7 w + 1 ∣ = 0

Apply absolute rule: If

∣ u ∣ = 0

then

u = 0

7 w + 1 = 0

7 w + 1 = 0 : w = - \frac{1}{7}

w = - \frac{1}{7}

\frac{1}{4} - 2 ∣ x + 2 ∣ = 0

x^{2} + 7 x + 14 = 4

∣ 2 x - 1 ∣ + x = 8

- 2 ∣ 7 - 3 x ∣ - 6 = - 14

x^{2} + 5 x = ∣ 4 - x ∣