Solve 31/2-2x(1/5)^2-221/3

$$3 \frac { 1 } { 2 } - 2 x ( \frac { 1 } { 5 } ) ^ { 2 } - 22 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{2x}{25}-\frac{113}{6}$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-2x\times \left(\frac{1}{5}\right)^{2}-\frac{22\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-2x\times \left(\frac{1}{5}\right)^{2}-\frac{22\times 3+1}{3}$$

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

$$\frac{7}{2}-2x\times \frac{1}{25}-\frac{22\times 3+1}{3}$$

Multiply 2 and \frac{1}{25} to get \frac{2}{25}.

$$\frac{7}{2}-\frac{2}{25}x-\frac{22\times 3+1}{3}$$

Multiply 22 and 3 to get 66.

$$\frac{7}{2}-\frac{2}{25}x-\frac{66+1}{3}$$

Add 66 and 1 to get 67.

$$\frac{7}{2}-\frac{2}{25}x-\frac{67}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{67}{3} to fractions with denominator 6.

$$\frac{21}{6}-\frac{2}{25}x-\frac{134}{6}$$

Since \frac{21}{6} and \frac{134}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-134}{6}-\frac{2}{25}x$$

Subtract 134 from 21 to get -113.

$$-\frac{113}{6}-\frac{2}{25}x$$

Expand

$$-\frac{2x}{25}-\frac{113}{6}$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-2x\times \left(\frac{1}{5}\right)^{2}-\frac{22\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-2x\times \left(\frac{1}{5}\right)^{2}-\frac{22\times 3+1}{3}$$

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

$$\frac{7}{2}-2x\times \frac{1}{25}-\frac{22\times 3+1}{3}$$

Multiply 2 and \frac{1}{25} to get \frac{2}{25}.

$$\frac{7}{2}-\frac{2}{25}x-\frac{22\times 3+1}{3}$$

Multiply 22 and 3 to get 66.

$$\frac{7}{2}-\frac{2}{25}x-\frac{66+1}{3}$$

Add 66 and 1 to get 67.

$$\frac{7}{2}-\frac{2}{25}x-\frac{67}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{67}{3} to fractions with denominator 6.

$$\frac{21}{6}-\frac{2}{25}x-\frac{134}{6}$$

Since \frac{21}{6} and \frac{134}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-134}{6}-\frac{2}{25}x$$

Subtract 134 from 21 to get -113.

$$-\frac{113}{6}-\frac{2}{25}x$$