Solve 11(23/11)-1/14=7(23/14)+10/6

$$\frac { 11 ( \frac { 23 } { 11 } ) - 1 } { 14 } = \frac { 7 ( \frac { 23 } { 14 } ) + 10 } { 6 }$$

Verify

Solution Steps

Multiply both sides of the equation by 42, the least common multiple of 14,6.

$$3\left(11\times \frac{23}{11}-1\right)=7\left(7\times \frac{23}{14}+10\right)$$

Cancel out 11 and 11.

$$3\left(23-1\right)=7\left(7\times \frac{23}{14}+10\right)$$

Subtract 1 from 23 to get 22.

$$3\times 22=7\left(7\times \frac{23}{14}+10\right)$$

Multiply 3 and 22 to get 66.

$$66=7\left(7\times \frac{23}{14}+10\right)$$

Express 7\times \frac{23}{14} as a single fraction.

$$66=7\left(\frac{7\times 23}{14}+10\right)$$

Multiply 7 and 23 to get 161.

$$66=7\left(\frac{161}{14}+10\right)$$

Reduce the fraction \frac{161}{14} to lowest terms by extracting and canceling out 7.

$$66=7\left(\frac{23}{2}+10\right)$$

Convert 10 to fraction \frac{20}{2}.

$$66=7\left(\frac{23}{2}+\frac{20}{2}\right)$$

Since \frac{23}{2} and \frac{20}{2} have the same denominator, add them by adding their numerators.

$$66=7\times \frac{23+20}{2}$$

Add 23 and 20 to get 43.

$$66=7\times \frac{43}{2}$$

Express 7\times \frac{43}{2} as a single fraction.

$$66=\frac{7\times 43}{2}$$

Multiply 7 and 43 to get 301.

$$66=\frac{301}{2}$$

Convert 66 to fraction \frac{132}{2}.

$$\frac{132}{2}=\frac{301}{2}$$

Compare \frac{132}{2} and \frac{301}{2}.

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