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

The solution to |x-4|+2|x-3|>= 4 is x = 14/3

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

∣ x - 4 ∣ + 2 ∣ x - 3 ∣ \geq 4

x \leq 2 or x \geq \frac{14}{3}

Interval Notation

(- \infty, 2] \cup [\frac{14}{3}, \infty)

Decimal Notation

x \leq 2 or x \geq 4.66666 \dots

Solution steps

∣ x - 4 ∣ + 2 ∣ x - 3 ∣ \geq 4

Find positive and negative intervals

x < 3, 3 \leq x < 4, x \geq 4

Solve the inequality for each interval

x \leq 2 or No Solution or x \geq \frac{14}{3}

Merge Overlapping Intervals

x \leq 2 or x \geq \frac{14}{3}

∣ 2 x + 7 ∣ < ∣ 5 ∣

(1 + x^{2}) \geq 1 - x^{2}

∣ x + 1 ∣ + ∣ x - 4 ∣ > 7

∣ m - 1 ∣ > ∣ m + 3 ∣

\frac{1}{5 ∣ 10 x - 2 ∣} < 1

What is |x-4|+2|x-3|>= 4 ?
The solution to |x-4|+2|x-3|>= 4 is x<= 2\lor x>= 14/3