Solve [(2-2/7)*(1+1/6)]^2-(6/3:2)*(1+2/3)+(frac{1}{2})^2=frac{13}{4}

$$[ ( 2 - \frac { 2 } { 7 } ) \cdot ( 1 + \frac { 1 } { 6 } ) ] ^ { 2 } - ( \frac { 6 } { 3 } : 2 ) \cdot ( 1 + \frac { 2 } { 3 } ) + ( \frac { 1 } { 2 } ) ^ { 2 } = \frac { 13 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$12\left(\left(\left(2-\frac{2}{7}\right)\left(1+\frac{1}{6}\right)\right)^{2}-\frac{\frac{6}{3}}{2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Subtract \frac{2}{7} from 2 to get \frac{12}{7}.

$$12\left(\left(\frac{12}{7}\left(1+\frac{1}{6}\right)\right)^{2}-\frac{\frac{6}{3}}{2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$12\left(\left(\frac{12}{7}\times \frac{7}{6}\right)^{2}-\frac{\frac{6}{3}}{2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Multiply \frac{12}{7} and \frac{7}{6} to get 2.

$$12\left(2^{2}-\frac{\frac{6}{3}}{2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Calculate 2 to the power of 2 and get 4.

$$12\left(4-\frac{\frac{6}{3}}{2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Express \frac{\frac{6}{3}}{2} as a single fraction.

$$12\left(4-\frac{6}{3\times 2}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Multiply 3 and 2 to get 6.

$$12\left(4-\frac{6}{6}\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Divide 6 by 6 to get 1.

$$12\left(4-1\left(1+\frac{2}{3}\right)\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$12\left(4-1\times \frac{5}{3}\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Multiply 1 and \frac{5}{3} to get \frac{5}{3}.

$$12\left(4-\frac{5}{3}\right)+12\times \left(\frac{1}{2}\right)^{2}=39$$

Subtract \frac{5}{3} from 4 to get \frac{7}{3}.

$$12\times \frac{7}{3}+12\times \left(\frac{1}{2}\right)^{2}=39$$

Multiply 12 and \frac{7}{3} to get 28.

$$28+12\times \left(\frac{1}{2}\right)^{2}=39$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$28+12\times \frac{1}{4}=39$$

Multiply 12 and \frac{1}{4} to get 3.

$$28+3=39$$

Add 28 and 3 to get 31.

$$31=39$$

Compare 31 and 39.

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