What is 1.05>(1+10w^2)/(1+w^2) ?

The solution to 1.05>(1+10w^2)/(1+w^2) is -1/(sqrt(179))<w< 1/(sqrt(179))

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1.05>(1+10w^2)/(1+w^2)

1.05 > \frac{1 + 10 w ^{2}}{1 + w ^{2}}

- \frac{1}{179} < w < \frac{1}{179}

Interval Notation

(- \frac{1}{179}, \frac{1}{179})

Decimal Notation

- 0.07474 \dots < w < 0.07474 \dots

Solution steps

1.05 > \frac{1 + 10 w ^{2}}{1 + w ^{2}}

Switch sides

\frac{1 + 10 w ^{2}}{1 + w ^{2}} < 1.05

Rewrite in standard form

\frac{1 + 10 w ^{2}}{1 + w ^{2}} - 1.05 < 0

Identify the intervals

- \frac{1}{179} < w < \frac{1}{179}

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What is 1.05>(1+10w^2)/(1+w^2) ?
The solution to 1.05>(1+10w^2)/(1+w^2) is -1/(sqrt(179))<w< 1/(sqrt(179))