What is 2<= |4-x|<7 ?

The solution to 2<= |4-x|<7 is -3<x<= 2\lor 6<= x<11

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2<= |4-x|<7

2 \leq ∣ 4 - x ∣ < 7

- 3 < x \leq 2 or 6 \leq x < 11

Interval Notation

(- 3, 2] \cup [6, 11)

Solution steps

2 \leq ∣ 4 - x ∣ < 7

a \leq u < b

then

a \leq u and u < b

2 \leq ∣ 4 - x ∣ and ∣ 4 - x ∣ < 7

2 \leq ∣ 4 - x ∣ : x \leq 2 or x \geq 6

∣ 4 - x ∣ < 7 : - 3 < x < 11

Combine the intervals

(x \leq 2 or x \geq 6) and - 3 < x < 11

Merge Overlapping Intervals

- 3 < x \leq 2 or 6 \leq x < 11

0 \leq 2 x^{2} + 5 x - 3

3 (8 - 2 x) = 6 (x + 4)

45 \cdot 4

1^{\frac{3}{4}}

\frac{12 w ^{9} v ^{4}}{( 4 w v ) ^{2}}