Solve 24/1-25^-7leq1/5^-2-6

$$\frac { 24 } { 1 - 25 ^ { - 7 } } \leq \frac { 1 } { 5 ^ { - 2 } - 6 }$$

Verify

Solution Steps

Calculate 25 to the power of -7 and get \frac{1}{6103515625}.

$$\frac{24}{1-\frac{1}{6103515625}}\leq \frac{1}{5^{-2}-6}$$

Subtract \frac{1}{6103515625} from 1 to get \frac{6103515624}{6103515625}.

$$\frac{24}{\frac{6103515624}{6103515625}}\leq \frac{1}{5^{-2}-6}$$

Divide 24 by \frac{6103515624}{6103515625} by multiplying 24 by the reciprocal of \frac{6103515624}{6103515625}.

$$24\times \frac{6103515625}{6103515624}\leq \frac{1}{5^{-2}-6}$$

Multiply 24 and \frac{6103515625}{6103515624} to get \frac{6103515625}{254313151}.

$$\frac{6103515625}{254313151}\leq \frac{1}{5^{-2}-6}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{6103515625}{254313151}\leq \frac{1}{\frac{1}{25}-6}$$

Subtract 6 from \frac{1}{25} to get -\frac{149}{25}.

$$\frac{6103515625}{254313151}\leq \frac{1}{-\frac{149}{25}}$$

Divide 1 by -\frac{149}{25} by multiplying 1 by the reciprocal of -\frac{149}{25}.

$$\frac{6103515625}{254313151}\leq 1\left(-\frac{25}{149}\right)$$

Multiply 1 and -\frac{25}{149} to get -\frac{25}{149}.

$$\frac{6103515625}{254313151}\leq -\frac{25}{149}$$

Least common multiple of 254313151 and 149 is 37892659499. Convert \frac{6103515625}{254313151} and -\frac{25}{149} to fractions with denominator 37892659499.

$$\frac{909423828125}{37892659499}\leq -\frac{6357828775}{37892659499}$$

Compare \frac{909423828125}{37892659499} and -\frac{6357828775}{37892659499}.

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