Solve 3/4x-1/2+7/4x+6/5

$$\frac{ 3 }{ 4 } x- \frac{ 1 }{ 2 } + \frac{ 7 }{ 4 } x+ \frac{ 6 }{ 5 }$$

Evaluate

$$\frac{5x}{2}+\frac{7}{10}$$

Solution Steps

Combine \frac{3}{4}x and \frac{7}{4}x to get \frac{5}{2}x.

$$\frac{5}{2}x-\frac{1}{2}+\frac{6}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{6}{5} to fractions with denominator 10.

$$\frac{5}{2}x-\frac{5}{10}+\frac{12}{10}$$

Since -\frac{5}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$\frac{5}{2}x+\frac{-5+12}{10}$$

Add -5 and 12 to get 7.

$$\frac{5}{2}x+\frac{7}{10}$$

Factor

$$\frac{25x+7}{10}$$

Solution Steps

Factor out \frac{1}{20}.

$$\frac{50x+14}{20}$$

Consider 15x-10+35x+24. Multiply and combine like terms.

$$50x+14$$

Consider 50x+14. Factor out 2.

$$2\left(25x+7\right)$$

Rewrite the complete factored expression.

$$\frac{25x+7}{10}$$