What is -4x+14+10|x-2|<12 ?

The solution to -4x+14+10|x-2|<12 is 11/7 <x<3

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-4x+14+10|x-2|<12

- 4 x + 14 + 10 ∣ x - 2 ∣ < 12

\frac{11}{7} < x < 3

Interval Notation

(\frac{11}{7}, 3)

Decimal Notation

1.57142 \dots < x < 3

Solution steps

- 4 x + 14 + 10 ∣ x - 2 ∣ < 12

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

\frac{11}{7} < x < 2 or 2 \leq x < 3

Merge Overlapping Intervals

\frac{11}{7} < x < 3

∣ x + 2 ∣ \leq x + 3

∣ x ∣ > 2 x + 7

\frac{3 - 5}{( 2 x - 6 )} \leq 7

∣ x - 1 ∣ + ∣ x - 3 ∣ > 2

\frac{( x - 2 )}{( x + 4 )} \leq \frac{( x + 3 )}{( x - 6 )}