Solve 2/5+12/5-8-2x/3+x+3/2

$$\frac { 2 } { 5 } + \frac { 12 } { 5 } - \frac { 8 - 2 x } { 3 } + \frac { x + 3 } { 2 }$$

Evaluate

$$\frac{7x}{6}+\frac{49}{30}$$

Short Solution Steps

Since \frac{2}{5} and \frac{12}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+12}{5}-\frac{8-2x}{3}+\frac{x+3}{2}$$

Add 2 and 12 to get 14.

$$\frac{14}{5}-\frac{8-2x}{3}+\frac{x+3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{14}{5} times \frac{3}{3}. Multiply \frac{8-2x}{3} times \frac{5}{5}.

$$\frac{14\times 3}{15}-\frac{5\left(8-2x\right)}{15}+\frac{x+3}{2}$$

Since \frac{14\times 3}{15} and \frac{5\left(8-2x\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14\times 3-5\left(8-2x\right)}{15}+\frac{x+3}{2}$$

Do the multiplications in 14\times 3-5\left(8-2x\right).

$$\frac{42-40+10x}{15}+\frac{x+3}{2}$$

Combine like terms in 42-40+10x.

$$\frac{2+10x}{15}+\frac{x+3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 2 is 30. Multiply \frac{2+10x}{15} times \frac{2}{2}. Multiply \frac{x+3}{2} times \frac{15}{15}.

$$\frac{2\left(2+10x\right)}{30}+\frac{15\left(x+3\right)}{30}$$

Since \frac{2\left(2+10x\right)}{30} and \frac{15\left(x+3\right)}{30} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2+10x\right)+15\left(x+3\right)}{30}$$

Do the multiplications in 2\left(2+10x\right)+15\left(x+3\right).

$$\frac{4+20x+15x+45}{30}$$

Combine like terms in 4+20x+15x+45.

$$\frac{49+35x}{30}$$

Expand

$$\frac{7x}{6}+\frac{49}{30}$$

Short Solution Steps

Since \frac{2}{5} and \frac{12}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+12}{5}-\frac{8-2x}{3}+\frac{x+3}{2}$$

Add 2 and 12 to get 14.

$$\frac{14}{5}-\frac{8-2x}{3}+\frac{x+3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{14}{5} times \frac{3}{3}. Multiply \frac{8-2x}{3} times \frac{5}{5}.

$$\frac{14\times 3}{15}-\frac{5\left(8-2x\right)}{15}+\frac{x+3}{2}$$

Since \frac{14\times 3}{15} and \frac{5\left(8-2x\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14\times 3-5\left(8-2x\right)}{15}+\frac{x+3}{2}$$

Do the multiplications in 14\times 3-5\left(8-2x\right).

$$\frac{42-40+10x}{15}+\frac{x+3}{2}$$

Combine like terms in 42-40+10x.

$$\frac{2+10x}{15}+\frac{x+3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 2 is 30. Multiply \frac{2+10x}{15} times \frac{2}{2}. Multiply \frac{x+3}{2} times \frac{15}{15}.

$$\frac{2\left(2+10x\right)}{30}+\frac{15\left(x+3\right)}{30}$$

Since \frac{2\left(2+10x\right)}{30} and \frac{15\left(x+3\right)}{30} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2+10x\right)+15\left(x+3\right)}{30}$$

Do the multiplications in 2\left(2+10x\right)+15\left(x+3\right).

$$\frac{4+20x+15x+45}{30}$$

Combine like terms in 4+20x+15x+45.

$$\frac{49+35x}{30}$$