What is (|7x+2|)/3 >5(8) ?

The solution to (|7x+2|)/3 >5(8) is x 118/7

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(|7x+2|)/3 >5(8)

\frac{∣ 7 x + 2 ∣}{3} > 5 (8)

x < - \frac{122}{7} or x > \frac{118}{7}

Interval Notation

(- \infty, - \frac{122}{7}) \cup (\frac{118}{7}, \infty)

Decimal Notation

x < - 17.42857 \dots or x > 16.85714 \dots

Solution steps

\frac{∣ 7 x + 2 ∣}{3} > 5 \cdot 8

Multiply the numbers:

5 \cdot 8 = 40

\frac{∣ 7 x + 2 ∣}{3} > 40

Multiply both sides by

3

∣ 7 x + 2 ∣ > 120

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

7 x + 2 < - 120 or 7 x + 2 > 120

7 x + 2 < - 120 or 7 x + 2 > 120

x < - \frac{122}{7} or x > \frac{118}{7}

- y^{2} + \frac{17}{4} y - 1 = 0

8 x^{2} - 98 = 0

x - 3 (x - 6) \leq 4 x

3 x^{2} - 6 x + 7 = 0

- 2 x + 5 > 16

What is (|7x+2|)/3 >5(8) ?
The solution to (|7x+2|)/3 >5(8) is x<-122/7 \lor x> 118/7