What is the answer to 3|x-4|=7 ?

The answer to 3|x-4|=7 is x= 5/3 \lor x= 19/3

Solve for x: 3|x-4|=7

The solution is x= 5/3 \lor x= 19/3

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3 ∣ x - 4 ∣ = 7

x = \frac{5}{3} or x = \frac{19}{3}

Decimal Notation

x = 1.66666 \dots, x = 6.33333 \dots

Solution steps

3 ∣ x - 4 ∣ = 7

Divide both sides by

3

∣ x - 4 ∣ = \frac{7}{3}

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

x - 4 = - \frac{7}{3} or x - 4 = \frac{7}{3}

x - 4 = - \frac{7}{3} or x - 4 = \frac{7}{3}

x = \frac{5}{3} or x = \frac{19}{3}

3 ∣ x - 4 ∣ = 9

6 ∣ y ∣ = 42

∣ u ∣ + 15 = 19

- ∣ 3 + x ∣ = 2

- ∣ 3 + x ∣ = 0