Solve 8x+1/2*3x/2+2/3

$$8 x + \frac { 1 } { 2 } \cdot \frac { 3 x } { 2 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{35x}{4}+\frac{2}{3}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{3x}{2} by multiplying numerator times numerator and denominator times denominator.

$$8x+\frac{3x}{2\times 2}+\frac{2}{3}$$

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

$$8x+\frac{3\times 3x}{12}+\frac{2\times 4}{12}$$

Since \frac{3\times 3x}{12} and \frac{2\times 4}{12} have the same denominator, add them by adding their numerators.

$$8x+\frac{3\times 3x+2\times 4}{12}$$

Do the multiplications in 3\times 3x+2\times 4.

$$8x+\frac{9x+8}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x times \frac{12}{12}.

$$\frac{12\times 8x}{12}+\frac{9x+8}{12}$$

Since \frac{12\times 8x}{12} and \frac{9x+8}{12} have the same denominator, add them by adding their numerators.

$$\frac{12\times 8x+9x+8}{12}$$

Do the multiplications in 12\times 8x+9x+8.

$$\frac{96x+9x+8}{12}$$

Combine like terms in 96x+9x+8.

$$\frac{105x+8}{12}$$

Factor

$$\frac{105x+8}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{96x+9x+8}{12}$$

Consider 96x+9x+8. Multiply and combine like terms.

$$105x+8$$

Rewrite the complete factored expression.

$$\frac{105x+8}{12}$$