What is |(x-1)/4+(x+2)/2 |<10 ?

The solution to |(x-1)/4+(x+2)/2 |<10 is -43/3 <x< 37/3

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|(x-1)/4+(x+2)/2 |<10

\frac{x - 1}{4} + \frac{x + 2}{2} < 10

- \frac{43}{3} < x < \frac{37}{3}

Interval Notation

(- \frac{43}{3}, \frac{37}{3})

Decimal Notation

- 14.33333 \dots < x < 12.33333 \dots

Solution steps

\frac{x - 1}{4} + \frac{x + 2}{2} < 10

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 10 < \frac{x - 1}{4} + \frac{x + 2}{2} < 10

\frac{x - 1}{4} + \frac{x + 2}{2} > - 10 and \frac{x - 1}{4} + \frac{x + 2}{2} < 10

x > - \frac{43}{3} and x < \frac{37}{3}

Merge Overlapping Intervals

- \frac{43}{3} < x < \frac{37}{3}

- 8 < 3 x - 9 < 9

\frac{x ^{2} + 5 x}{x ^{2} - 36} \leq 0

- 3 - x = - 5

a^{3} - 2 a^{2}

7 \cdot 4

What is |(x-1)/4+(x+2)/2 |<10 ?
The solution to |(x-1)/4+(x+2)/2 |<10 is -43/3 <x< 37/3