What is 3|x-1|+2|x-2|+|x-3|>4 ?

The solution to 3|x-1|+2|x-2|+|x-3|>4 is x 2

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3|x-1|+2|x-2|+|x-3|>4

3 ∣ x - 1 ∣ + 2 ∣ x - 2 ∣ + ∣ x - 3 ∣ > 4

x < 1 or x > 2

Interval Notation

(- \infty, 1) \cup (2, \infty)

Solution steps

3 ∣ x - 1 ∣ + 2 ∣ x - 2 ∣ + ∣ x - 3 ∣ > 4

Find positive and negative intervals

x < 1, 1 \leq x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

x < 1 or No Solution or 2 < x < 3 or x \geq 3

Merge Overlapping Intervals

x < 1 or x > 2

\frac{( 3 x - 4 )}{2} < \frac{5}{12}

\frac{( x + 1 )}{( x - 3 )} < \frac{1}{3}

∣ x + 1 ∣ + ∣ x + 2 ∣ \leq 10

\frac{3 ∣ x ∣ - 2}{∣ x ∣ - 1} \geq 2

x ∣ x + 1 ∣ + ∣ x ∣ > 3

What is 3|x-1|+2|x-2|+|x-3|>4 ?
The solution to 3|x-1|+2|x-2|+|x-3|>4 is x<1\lor x>2