What is -2|7d|+9>=-7 ?

The solution to -2|7d|+9>=-7 is -8/7 <= d<= 8/7

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-2|7d|+9>=-7

- 2 ∣ 7 d ∣ + 9 \geq - 7

- \frac{8}{7} \leq d \leq \frac{8}{7}

Interval Notation

[- \frac{8}{7}, \frac{8}{7}]

Decimal Notation

- 1.14285 \dots \leq d \leq 1.14285 \dots

Solution steps

- 2 ∣ 7 d ∣ + 9 \geq - 7

Move

9

to the right side

- 2 ∣ 7 d ∣ \geq - 16

Multiply both sides by

- 1

2 ∣ 7 d ∣ \leq 16

Divide both sides by

2

∣ 7 d ∣ \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq 7 d \leq 8

7 d \geq - 8 and 7 d \leq 8

d \geq - \frac{8}{7} and d \leq \frac{8}{7}

Merge Overlapping Intervals

- \frac{8}{7} \leq d \leq \frac{8}{7}

3 (3 x - 8) = 4 x + 6

5 x + 6 = 3 (- x - 1)

0 = - (x - 3)^{2} + 1

10 - 2 (\frac{1}{2})

2 x^{2} - 5 x - 9 = 0