Solve {l}{-2(5/4+1)+6(5/4)-3=-4(5/4)+5}{-2(5+4/4)+frac{30}{4}-3=-frac{20}{4}+5}

$$\left. \begin{array} { l } { - 2 ( \frac { 5 } { 4 } + 1 ) + 6 ( \frac { 5 } { 4 } ) - 3 = - 4 ( \frac { 5 } { 4 } ) + 5 } \\ { - 2 ( \frac { 5 + 4 } { 4 } ) + \frac { 30 } { 4 } - 3 = - \frac { 20 } { 4 } + 5 } \end{array} \right.$$

Verify

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$-2\left(\frac{5}{4}+\frac{4}{4}\right)+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$-2\times \frac{5+4}{4}+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Add 5 and 4 to get 9.

$$-2\times \frac{9}{4}+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Express -2\times \frac{9}{4} as a single fraction.

$$\frac{-2\times 9}{4}+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Multiply -2 and 9 to get -18.

$$\frac{-18}{4}+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{9}{2}+6\times \frac{5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Express 6\times \frac{5}{4} as a single fraction.

$$-\frac{9}{2}+\frac{6\times 5}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Multiply 6 and 5 to get 30.

$$-\frac{9}{2}+\frac{30}{4}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{9}{2}+\frac{15}{2}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Since -\frac{9}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{-9+15}{2}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Add -9 and 15 to get 6.

$$\frac{6}{2}-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Divide 6 by 2 to get 3.

$$3-3=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Subtract 3 from 3 to get 0.

$$0=-4\times \frac{5}{4}+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Multiply -4 times \frac{5}{4}.

$$0=-5+5\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Add -5 and 5 to get 0.

$$0=0\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Compare 0 and 0.

$$\text{true}\text{ and }-2\times \frac{5+4}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Add 5 and 4 to get 9.

$$\text{true}\text{ and }-2\times \frac{9}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Express -2\times \frac{9}{4} as a single fraction.

$$\text{true}\text{ and }\frac{-2\times 9}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Multiply -2 and 9 to get -18.

$$\text{true}\text{ and }\frac{-18}{4}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

$$\text{true}\text{ and }-\frac{9}{2}+\frac{30}{4}-3=-\frac{20}{4}+5$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\text{true}\text{ and }-\frac{9}{2}+\frac{15}{2}-3=-\frac{20}{4}+5$$

Since -\frac{9}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{-9+15}{2}-3=-\frac{20}{4}+5$$

Add -9 and 15 to get 6.

$$\text{true}\text{ and }\frac{6}{2}-3=-\frac{20}{4}+5$$

Divide 6 by 2 to get 3.

$$\text{true}\text{ and }3-3=-\frac{20}{4}+5$$

Subtract 3 from 3 to get 0.

$$\text{true}\text{ and }0=-\frac{20}{4}+5$$

Divide 20 by 4 to get 5.

$$\text{true}\text{ and }0=-5+5$$

Add -5 and 5 to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$