What is (x-3)<(x-2)<(x-1) ?

The solution to (x-3)<(x-2)<(x-1) is True for all x

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(x-3)<(x-2)<(x-1)

(x - 3) < (x - 2) < (x - 1)

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

(x - 3) < (x - 2) < (x - 1)

a < u < b

then

a < u and u < b

(x - 3) < (x - 2) and (x - 2) < (x - 1)

x - 3 < x - 2 :

True for all

x

x - 2 < x - 1 :

True for all

x

Combine the intervals

True for all x and True for all x

Merge Overlapping Intervals

True for all x

- 8 < x < 0

\frac{1}{3 \cdot ( x - 1 )} < \frac{1}{4} \cdot (x + 2) < \frac{1}{6 \cdot ( x + 4 )}

2 \leq - 3 x - 13 < 8

9 < 4 x + 1 \leq 33

- 6 < x + 3 < 2