Solve B=a-1/3+a+1/4-1

$$B = \frac { a - 1 } { 3 } + \frac { a + 1 } { 4 } - 1$$

Solve for B

$$B=\frac{7a-13}{12}$$

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{a-1}{3} times \frac{4}{4}. Multiply \frac{a+1}{4} times \frac{3}{3}.

$$B=\frac{4\left(a-1\right)}{12}+\frac{3\left(a+1\right)}{12}-1$$

Since \frac{4\left(a-1\right)}{12} and \frac{3\left(a+1\right)}{12} have the same denominator, add them by adding their numerators.

$$B=\frac{4\left(a-1\right)+3\left(a+1\right)}{12}-1$$

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

$$B=\frac{4a-4+3a+3}{12}-1$$

Combine like terms in 4a-4+3a+3.

$$B=\frac{7a-1}{12}-1$$

Divide each term of 7a-1 by 12 to get \frac{7}{12}a-\frac{1}{12}.

$$B=\frac{7}{12}a-\frac{1}{12}-1$$

Subtract 1 from -\frac{1}{12} to get -\frac{13}{12}.

$$B=\frac{7}{12}a-\frac{13}{12}$$

Solve for a

$$a=\frac{12B+13}{7}$$

Steps for Solving Linear Equation

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

$$B=\frac{4\left(a-1\right)}{12}+\frac{3\left(a+1\right)}{12}-1$$

Since \frac{4\left(a-1\right)}{12} and \frac{3\left(a+1\right)}{12} have the same denominator, add them by adding their numerators.

$$B=\frac{4\left(a-1\right)+3\left(a+1\right)}{12}-1$$

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

$$B=\frac{4a-4+3a+3}{12}-1$$

Combine like terms in 4a-4+3a+3.

$$B=\frac{7a-1}{12}-1$$

Divide each term of 7a-1 by 12 to get \frac{7}{12}a-\frac{1}{12}.

$$B=\frac{7}{12}a-\frac{1}{12}-1$$

Subtract 1 from -\frac{1}{12} to get -\frac{13}{12}.

$$B=\frac{7}{12}a-\frac{13}{12}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{7}{12}a-\frac{13}{12}=B$$

Add \frac{13}{12} to both sides.

$$\frac{7}{12}a=B+\frac{13}{12}$$

Divide both sides of the equation by \frac{7}{12}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{7}{12}a}{\frac{7}{12}}=\frac{B+\frac{13}{12}}{\frac{7}{12}}$$

Dividing by \frac{7}{12} undoes the multiplication by \frac{7}{12}.

$$a=\frac{B+\frac{13}{12}}{\frac{7}{12}}$$

Divide B+\frac{13}{12} by \frac{7}{12} by multiplying B+\frac{13}{12} by the reciprocal of \frac{7}{12}.

$$a=\frac{12B+13}{7}$$