What is 7|-5v+4|+6<61 ?

The solution to 7|-5v+4|+6<61 is -27/35 <v< 83/35

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7|-5v+4|+6<61

7 ∣ - 5 v + 4 ∣ + 6 < 61

- \frac{27}{35} < v < \frac{83}{35}

Interval Notation

(- \frac{27}{35}, \frac{83}{35})

Decimal Notation

- 0.77142 \dots < v < 2.37142 \dots

Solution steps

7 ∣ - 5 v + 4 ∣ + 6 < 61

Move

6

to the right side

7 ∣ - 5 v + 4 ∣ < 55

Divide both sides by

7

∣ - 5 v + 4 ∣ < \frac{55}{7}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{55}{7} < - 5 v + 4 < \frac{55}{7}

- 5 v + 4 > - \frac{55}{7} and - 5 v + 4 < \frac{55}{7}

v < \frac{83}{35} and v > - \frac{27}{35}

Merge Overlapping Intervals

- \frac{27}{35} < v < \frac{83}{35}

2 \leq x + 9 < 6

(3 z - 4) (5 z + 4)^{2} + (3 z - 4)^{2} (5 z + 4)

\frac{9}{2} + \frac{1}{2}

\frac{3 x + 1}{x - 4} \geq \frac{1}{3}

4 x^{2} + x - 5