Solve 1/2a+2/3x-3/4a+5/6x+frac{3}{8}a-frac{7}{12}

$$\frac{ 1 }{ 2 } a+ \frac{ 2 }{ 3 } x- \frac{ 3 }{ 4 } a+ \frac{ 5 }{ 6 } x+ \frac{ 3 }{ 8 } a- \frac{ 7 }{ 12 }$$

Evaluate

$$\frac{a}{8}+\frac{3x}{2}-\frac{7}{12}$$

Solution Steps

Combine \frac{1}{2}a and -\frac{3}{4}a to get -\frac{1}{4}a.

$$-\frac{1}{4}a+\frac{2}{3}x+\frac{5}{6}x+\frac{3}{8}a-\frac{7}{12}$$

Combine \frac{2}{3}x and \frac{5}{6}x to get \frac{3}{2}x.

$$-\frac{1}{4}a+\frac{3}{2}x+\frac{3}{8}a-\frac{7}{12}$$

Combine -\frac{1}{4}a and \frac{3}{8}a to get \frac{1}{8}a.

$$\frac{1}{8}a+\frac{3}{2}x-\frac{7}{12}$$

Factor

$$\frac{36x+3a-14}{24}$$

Solution Steps

Factor out \frac{1}{24}.

$$\frac{12a+16x-18a+20x+9a-14}{24}$$

Consider 12a+16x-18a+20x+9a-14. Multiply and combine like terms.

$$36x+3a-14$$

Rewrite the complete factored expression.

$$\frac{36x+3a-14}{24}$$