What is (|90-x|)/(90)<5\times 10^{-3} ?

The solution to (|90-x|)/(90)<5\times 10^{-3} is 1791/20 <x< 1809/20

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(|90-x|)/(90)<5\times 10^{-3}

\frac{∣ 90 - x ∣}{90} < 5 \cdot 1 0^{- 3}

\frac{1791}{20} < x < \frac{1809}{20}

Interval Notation

(\frac{1791}{20}, \frac{1809}{20})

Decimal Notation

89.55 < x < 90.45

Solution steps

\frac{∣ 90 - x ∣}{90} < 5 \cdot 1 0^{- 3}

Simplify

5 \cdot 1 0^{- 3} : \frac{1}{200}

\frac{∣ 90 - x ∣}{90} < \frac{1}{200}

Multiply both sides by

90

∣ 90 - x ∣ < \frac{9}{20}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{9}{20} < 90 - x < \frac{9}{20}

90 - x > - \frac{9}{20} and 90 - x < \frac{9}{20}

x < \frac{1809}{20} and x > \frac{1791}{20}

Merge Overlapping Intervals

\frac{1791}{20} < x < \frac{1809}{20}

\frac{- 3}{- 3}

(x - 3) (x + 2) < 0

- 2 x^{2} + 7 = 3 x + 8

7 x - (3 x + 5) > 2 (5 x - 4)

3 x^{2} + 26 x - 9

What is (|90-x|)/(90)<5\times 10^{-3} ?
The solution to (|90-x|)/(90)<5\times 10^{-3} is 1791/20 <x< 1809/20