What is 7+|6v+7|<= 60 ?

The solution to 7+|6v+7|<= 60 is -10<= v<= 23/3

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7+|6v+7|<= 60

7 + ∣ 6 v + 7 ∣ \leq 60

- 10 \leq v \leq \frac{23}{3}

Interval Notation

[- 10, \frac{23}{3}]

Decimal Notation

- 10 \leq v \leq 7.66666 \dots

Solution steps

7 + ∣ 6 v + 7 ∣ \leq 60

Move

7

to the right side

∣ 6 v + 7 ∣ \leq 53

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 53 \leq 6 v + 7 \leq 53

6 v + 7 \geq - 53 and 6 v + 7 \leq 53

v \geq - 10 and v \leq \frac{23}{3}

Merge Overlapping Intervals

- 10 \leq v \leq \frac{23}{3}

2 x^{2} + 5 x - 3

x^{2} - x^{2} \leq 0

3 d^{2} - 18 d - 48

1 7^{3}

m = - (4 + m) + 2