Solve 8(-97/49)+11/3=6(-97/46)-3/8

$$\frac { 8 ( - \frac { 97 } { 49 } ) + 11 } { 3 } = \frac { 6 ( - \frac { 97 } { 46 } ) - 3 } { 8 }$$

Verify

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 3,8.

$$8\left(8\left(-\frac{97}{49}\right)+11\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Express 8\left(-\frac{97}{49}\right) as a single fraction.

$$8\left(\frac{8\left(-97\right)}{49}+11\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Multiply 8 and -97 to get -776.

$$8\left(\frac{-776}{49}+11\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Fraction \frac{-776}{49} can be rewritten as -\frac{776}{49} by extracting the negative sign.

$$8\left(-\frac{776}{49}+11\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Convert 11 to fraction \frac{539}{49}.

$$8\left(-\frac{776}{49}+\frac{539}{49}\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Since -\frac{776}{49} and \frac{539}{49} have the same denominator, add them by adding their numerators.

$$8\times \frac{-776+539}{49}=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Add -776 and 539 to get -237.

$$8\left(-\frac{237}{49}\right)=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Express 8\left(-\frac{237}{49}\right) as a single fraction.

$$\frac{8\left(-237\right)}{49}=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Multiply 8 and -237 to get -1896.

$$\frac{-1896}{49}=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Fraction \frac{-1896}{49} can be rewritten as -\frac{1896}{49} by extracting the negative sign.

$$-\frac{1896}{49}=3\left(6\left(-\frac{97}{46}\right)-3\right)$$

Express 6\left(-\frac{97}{46}\right) as a single fraction.

$$-\frac{1896}{49}=3\left(\frac{6\left(-97\right)}{46}-3\right)$$

Multiply 6 and -97 to get -582.

$$-\frac{1896}{49}=3\left(\frac{-582}{46}-3\right)$$

Reduce the fraction \frac{-582}{46} to lowest terms by extracting and canceling out 2.

$$-\frac{1896}{49}=3\left(-\frac{291}{23}-3\right)$$

Convert 3 to fraction \frac{69}{23}.

$$-\frac{1896}{49}=3\left(-\frac{291}{23}-\frac{69}{23}\right)$$

Since -\frac{291}{23} and \frac{69}{23} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1896}{49}=3\times \frac{-291-69}{23}$$

Subtract 69 from -291 to get -360.

$$-\frac{1896}{49}=3\left(-\frac{360}{23}\right)$$

Express 3\left(-\frac{360}{23}\right) as a single fraction.

$$-\frac{1896}{49}=\frac{3\left(-360\right)}{23}$$

Multiply 3 and -360 to get -1080.

$$-\frac{1896}{49}=\frac{-1080}{23}$$

Fraction \frac{-1080}{23} can be rewritten as -\frac{1080}{23} by extracting the negative sign.

$$-\frac{1896}{49}=-\frac{1080}{23}$$

Least common multiple of 49 and 23 is 1127. Convert -\frac{1896}{49} and -\frac{1080}{23} to fractions with denominator 1127.

$$-\frac{43608}{1127}=-\frac{52920}{1127}$$

Compare -\frac{43608}{1127} and -\frac{52920}{1127}.

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