What is |x^2-10x+21|-|3x-15|<= 0 ?

The solution to |x^2-10x+21|-|3x-15|<= 0 is 1<= x<= 4\lor 6<= x<= 9

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|x^2-10x+21|-|3x-15|<= 0

x^{2} - 10 x + 21 - ∣ 3 x - 15 ∣ \leq 0

1 \leq x \leq 4 or 6 \leq x \leq 9

Interval Notation

[1, 4] \cup [6, 9]

Solution steps

x^{2} - 10 x + 21 - ∣ 3 x - 15 ∣ \leq 0

Find positive and negative intervals

x \leq 3, 3 < x < 5, 5 \leq x < 7, x \geq 7

Solve the inequality for each interval

1 \leq x \leq 3 or 3 < x \leq 4 or 6 \leq x < 7 or 7 \leq x \leq 9

Merge Overlapping Intervals

1 \leq x \leq 4 or 6 \leq x \leq 9

3 (x + 4) \geq 0 or 3 (x + 3) \leq 3

x^{2} - 4 x - 70 = 0

(3 x - 1)^{2} + 12 x - 4 = 0

\frac{4 ^{9}}{4 ^{5}}

\frac{3}{4} x + 1 < 4

What is |x^2-10x+21|-|3x-15|<= 0 ?
The solution to |x^2-10x+21|-|3x-15|<= 0 is 1<= x<= 4\lor 6<= x<= 9