Solve 5/3+13/4=13/7-21/2

$$\frac { 5 } { 3 } + 1 \frac { 3 } { 4 } = 1 \frac { 3 } { 7 } - 2 \frac { 1 } { 2 }$$

Verify

Solution Steps

Multiply both sides of the equation by 84, the least common multiple of 3,4,7,2.

$$140+21\left(1\times 4+3\right)=12\left(1\times 7+3\right)-42\left(2\times 2+1\right)$$

Multiply 1 and 4 to get 4.

$$140+21\left(4+3\right)=12\left(1\times 7+3\right)-42\left(2\times 2+1\right)$$

Add 4 and 3 to get 7.

$$140+21\times 7=12\left(1\times 7+3\right)-42\left(2\times 2+1\right)$$

Multiply 21 and 7 to get 147.

$$140+147=12\left(1\times 7+3\right)-42\left(2\times 2+1\right)$$

Add 140 and 147 to get 287.

$$287=12\left(1\times 7+3\right)-42\left(2\times 2+1\right)$$

Multiply 1 and 7 to get 7.

$$287=12\left(7+3\right)-42\left(2\times 2+1\right)$$

Add 7 and 3 to get 10.

$$287=12\times 10-42\left(2\times 2+1\right)$$

Multiply 12 and 10 to get 120.

$$287=120-42\left(2\times 2+1\right)$$

Multiply 2 and 2 to get 4.

$$287=120-42\left(4+1\right)$$

Add 4 and 1 to get 5.

$$287=120-42\times 5$$

Multiply -42 and 5 to get -210.

$$287=120-210$$

Subtract 210 from 120 to get -90.

$$287=-90$$

Compare 287 and -90.

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