What is 6|10-7x|-2<= 22 ?

The solution to 6|10-7x|-2<= 22 is 6/7 <= x<= 2

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6|10-7x|-2<= 22

6 ∣ 10 - 7 x ∣ - 2 \leq 22

\frac{6}{7} \leq x \leq 2

Interval Notation

[\frac{6}{7}, 2]

Decimal Notation

0.85714 \dots \leq x \leq 2

Solution steps

6 ∣ 10 - 7 x ∣ - 2 \leq 22

Move

2

to the right side

6 ∣ 10 - 7 x ∣ \leq 24

Divide both sides by

6

∣ 10 - 7 x ∣ \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq 10 - 7 x \leq 4

10 - 7 x \geq - 4 and 10 - 7 x \leq 4

x \leq 2 and x \geq \frac{6}{7}

Merge Overlapping Intervals

\frac{6}{7} \leq x \leq 2

10 x^{2} y^{3} - 5 x y^{3} + 2 x^{2} + 6 x^{3}

lo g_{9} (3)

3 x^{2} - 48 x + 180

6 - 2 x \geq - 14

4 g^{2} + 8 g + 4 = 0