Solve x+2/3-2x-1/4+1

$$\frac { x + 2 } { 3 } - \frac { 2 x - 1 } { 4 } + 1$$

Evaluate

$$-\frac{x}{6}+\frac{23}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{x+2}{3} times \frac{4}{4}. Multiply \frac{2x-1}{4} times \frac{3}{3}.

$$\frac{4\left(x+2\right)}{12}-\frac{3\left(2x-1\right)}{12}+1$$

Since \frac{4\left(x+2\right)}{12} and \frac{3\left(2x-1\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x+2\right)-3\left(2x-1\right)}{12}+1$$

Do the multiplications in 4\left(x+2\right)-3\left(2x-1\right).

$$\frac{4x+8-6x+3}{12}+1$$

Combine like terms in 4x+8-6x+3.

$$\frac{-2x+11}{12}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{12}{12}.

$$\frac{-2x+11}{12}+\frac{12}{12}$$

Since \frac{-2x+11}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{-2x+11+12}{12}$$

Combine like terms in -2x+11+12.

$$\frac{-2x+23}{12}$$

Expand

$$-\frac{x}{6}+\frac{23}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{x+2}{3} times \frac{4}{4}. Multiply \frac{2x-1}{4} times \frac{3}{3}.

$$\frac{4\left(x+2\right)}{12}-\frac{3\left(2x-1\right)}{12}+1$$

Since \frac{4\left(x+2\right)}{12} and \frac{3\left(2x-1\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x+2\right)-3\left(2x-1\right)}{12}+1$$

Do the multiplications in 4\left(x+2\right)-3\left(2x-1\right).

$$\frac{4x+8-6x+3}{12}+1$$

Combine like terms in 4x+8-6x+3.

$$\frac{-2x+11}{12}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{12}{12}.

$$\frac{-2x+11}{12}+\frac{12}{12}$$

Since \frac{-2x+11}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{-2x+11+12}{12}$$

Combine like terms in -2x+11+12.

$$\frac{-2x+23}{12}$$