Solve frac{(4-3^{2})^{2}-(-3)^2}{|7^2-54|+3}>4^2-7-(11-2)/(11-1)^2+5

$$\frac { ( 4 - 3 ^ { 2 } ) ^ { 2 } - ( - 3 ) ^ { 2 } } { | 7 ^ { 2 } - 54 | + 3 } > \frac { 4 ^ { 2 } - 7 - ( 11 - 2 ) } { ( 11 - 1 ) ^ { 2 } + 5 }$$

Verify

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(4-9\right)^{2}-\left(-3\right)^{2}}{|7^{2}-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Subtract 9 from 4 to get -5.

$$\frac{\left(-5\right)^{2}-\left(-3\right)^{2}}{|7^{2}-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Calculate -5 to the power of 2 and get 25.

$$\frac{25-\left(-3\right)^{2}}{|7^{2}-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{25-9}{|7^{2}-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Subtract 9 from 25 to get 16.

$$\frac{16}{|7^{2}-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{16}{|49-54|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Subtract 54 from 49 to get -5.

$$\frac{16}{|-5|+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -5 is 5.

$$\frac{16}{5+3}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Add 5 and 3 to get 8.

$$\frac{16}{8}>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Divide 16 by 8 to get 2.

$$2>\frac{4^{2}-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Calculate 4 to the power of 2 and get 16.

$$2>\frac{16-7-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Subtract 7 from 16 to get 9.

$$2>\frac{9-\left(11-2\right)}{\left(11-1\right)^{2}+5}$$

Subtract 2 from 11 to get 9.

$$2>\frac{9-9}{\left(11-1\right)^{2}+5}$$

Subtract 9 from 9 to get 0.

$$2>\frac{0}{\left(11-1\right)^{2}+5}$$

Subtract 1 from 11 to get 10.

$$2>\frac{0}{10^{2}+5}$$

Calculate 10 to the power of 2 and get 100.

$$2>\frac{0}{100+5}$$

Add 100 and 5 to get 105.

$$2>\frac{0}{105}$$

Zero divided by any non-zero number gives zero.

$$2>0$$

Compare 2 and 0.

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