What is -2|3x+4|+7>1 ?

The solution to -2|3x+4|+7>1 is -7/3 <x<-1/3

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-2|3x+4|+7>1

- 2 ∣ 3 x + 4 ∣ + 7 > 1

- \frac{7}{3} < x < - \frac{1}{3}

Interval Notation

(- \frac{7}{3}, - \frac{1}{3})

Decimal Notation

- 2.33333 \dots < x < - 0.33333 \dots

Solution steps

- 2 ∣ 3 x + 4 ∣ + 7 > 1

Move

7

to the right side

- 2 ∣ 3 x + 4 ∣ > - 6

Multiply both sides by

- 1

2 ∣ 3 x + 4 ∣ < 6

Divide both sides by

2

∣ 3 x + 4 ∣ < 3

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 3 < 3 x + 4 < 3

3 x + 4 > - 3 and 3 x + 4 < 3

x > - \frac{7}{3} and x < - \frac{1}{3}

Merge Overlapping Intervals

- \frac{7}{3} < x < - \frac{1}{3}

f = - (1)^{5}

5 \cdot 18

(2 x - 9 y) + (4 x + 7 b)

0 - 4 y = 8

\frac{3}{5} (3)