Solve 1-2-3/5+2a-1/2-3a-4/10=

$$1 - \frac { 2 - 3 } { 5 } + \frac { 2 a - 1 } { 2 } - \frac { 3 a - 4 } { 10 } =$$

Evaluate

$$\frac{7a+11}{10}$$

Short Solution Steps

Subtract 3 from 2 to get -1.

$$1-\frac{-1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$1-\left(-\frac{1}{5}\right)+\frac{2a-1}{2}-\frac{3a-4}{10}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$1+\frac{1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{5}+\frac{1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Add 5 and 1 to get 6.

$$\frac{6}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{6}{5} times \frac{2}{2}. Multiply \frac{2a-1}{2} times \frac{5}{5}.

$$\frac{6\times 2}{10}+\frac{5\left(2a-1\right)}{10}-\frac{3a-4}{10}$$

Since \frac{6\times 2}{10} and \frac{5\left(2a-1\right)}{10} have the same denominator, add them by adding their numerators.

$$\frac{6\times 2+5\left(2a-1\right)}{10}-\frac{3a-4}{10}$$

Do the multiplications in 6\times 2+5\left(2a-1\right).

$$\frac{12+10a-5}{10}-\frac{3a-4}{10}$$

Combine like terms in 12+10a-5.

$$\frac{7+10a}{10}-\frac{3a-4}{10}$$

Since \frac{7+10a}{10} and \frac{3a-4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7+10a-\left(3a-4\right)}{10}$$

Do the multiplications in 7+10a-\left(3a-4\right).

$$\frac{7+10a-3a+4}{10}$$

Combine like terms in 7+10a-3a+4.

$$\frac{11+7a}{10}$$

Expand

$$\frac{7a+11}{10}$$

Short Solution Steps

Subtract 3 from 2 to get -1.

$$1-\frac{-1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$1-\left(-\frac{1}{5}\right)+\frac{2a-1}{2}-\frac{3a-4}{10}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$1+\frac{1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{5}+\frac{1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

Add 5 and 1 to get 6.

$$\frac{6}{5}+\frac{2a-1}{2}-\frac{3a-4}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{6}{5} times \frac{2}{2}. Multiply \frac{2a-1}{2} times \frac{5}{5}.

$$\frac{6\times 2}{10}+\frac{5\left(2a-1\right)}{10}-\frac{3a-4}{10}$$

Since \frac{6\times 2}{10} and \frac{5\left(2a-1\right)}{10} have the same denominator, add them by adding their numerators.

$$\frac{6\times 2+5\left(2a-1\right)}{10}-\frac{3a-4}{10}$$

Do the multiplications in 6\times 2+5\left(2a-1\right).

$$\frac{12+10a-5}{10}-\frac{3a-4}{10}$$

Combine like terms in 12+10a-5.

$$\frac{7+10a}{10}-\frac{3a-4}{10}$$

Since \frac{7+10a}{10} and \frac{3a-4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7+10a-\left(3a-4\right)}{10}$$

Do the multiplications in 7+10a-\left(3a-4\right).

$$\frac{7+10a-3a+4}{10}$$

Combine like terms in 7+10a-3a+4.

$$\frac{11+7a}{10}$$