Solve B-A/2-frac{3{5k}}=7-2B

$$\frac{ B-A }{ 2- \frac{ 3 }{ 5k } } = 7-2B$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{21-70k-5Ak}{25k-6}\text{, }&k\neq \frac{6}{25}\text{ and }k\neq \frac{3}{10}\text{ and }k\neq 0\\B\in \mathrm{C}\text{, }&k=\frac{6}{25}\text{ and }A=\frac{7}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5k}{5k}.

$$\frac{B-A}{\frac{2\times 5k}{5k}-\frac{3}{5k}}=7-2B$$

Since \frac{2\times 5k}{5k} and \frac{3}{5k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{B-A}{\frac{2\times 5k-3}{5k}}=7-2B$$

Do the multiplications in 2\times 5k-3.

$$\frac{B-A}{\frac{10k-3}{5k}}=7-2B$$

Divide B-A by \frac{10k-3}{5k} by multiplying B-A by the reciprocal of \frac{10k-3}{5k}.

$$\frac{\left(B-A\right)\times 5k}{10k-3}=7-2B$$

Use the distributive property to multiply B-A by 5.

$$\frac{\left(5B-5A\right)k}{10k-3}=7-2B$$

Use the distributive property to multiply 5B-5A by k.

$$\frac{5Bk-5Ak}{10k-3}=7-2B$$

Add 2B to both sides.

$$\frac{5Bk-5Ak}{10k-3}+2B=7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2B times \frac{10k-3}{10k-3}.

$$\frac{5Bk-5Ak}{10k-3}+\frac{2B\left(10k-3\right)}{10k-3}=7$$

Since \frac{5Bk-5Ak}{10k-3} and \frac{2B\left(10k-3\right)}{10k-3} have the same denominator, add them by adding their numerators.

$$\frac{5Bk-5Ak+2B\left(10k-3\right)}{10k-3}=7$$

Do the multiplications in 5Bk-5Ak+2B\left(10k-3\right).

$$\frac{5Bk-5Ak+20Bk-6B}{10k-3}=7$$

Combine like terms in 5Bk-5Ak+20Bk-6B.

$$\frac{25Bk-5Ak-6B}{10k-3}=7$$

Multiply both sides of the equation by 10k-3.

$$25Bk-5Ak-6B=7\left(10k-3\right)$$

Use the distributive property to multiply 7 by 10k-3.

$$25Bk-5Ak-6B=70k-21$$

Add 5Ak to both sides.

$$25Bk-6B=70k-21+5Ak$$

Combine all terms containing B.

$$\left(25k-6\right)B=70k-21+5Ak$$

The equation is in standard form.

$$\left(25k-6\right)B=5Ak+70k-21$$

Divide both sides by 25k-6.

$$\frac{\left(25k-6\right)B}{25k-6}=\frac{5Ak+70k-21}{25k-6}$$

Dividing by 25k-6 undoes the multiplication by 25k-6.

$$B=\frac{5Ak+70k-21}{25k-6}$$

Solve for A

$$A=5B-\frac{6B}{5k}-14+\frac{21}{5k}$$

$$k\neq \frac{3}{10}\text{ and }k\neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5k}{5k}.

$$\frac{B-A}{\frac{2\times 5k}{5k}-\frac{3}{5k}}=7-2B$$

Since \frac{2\times 5k}{5k} and \frac{3}{5k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{B-A}{\frac{2\times 5k-3}{5k}}=7-2B$$

Do the multiplications in 2\times 5k-3.

$$\frac{B-A}{\frac{10k-3}{5k}}=7-2B$$

Divide B-A by \frac{10k-3}{5k} by multiplying B-A by the reciprocal of \frac{10k-3}{5k}.

$$\frac{\left(B-A\right)\times 5k}{10k-3}=7-2B$$

Use the distributive property to multiply B-A by 5.

$$\frac{\left(5B-5A\right)k}{10k-3}=7-2B$$

Use the distributive property to multiply 5B-5A by k.

$$\frac{5Bk-5Ak}{10k-3}=7-2B$$

Multiply both sides of the equation by 10k-3.

$$5Bk-5Ak=\left(10k-3\right)\times 7-2B\left(10k-3\right)$$

Use the distributive property to multiply 10k-3 by 7.

$$5Bk-5Ak=70k-21-2B\left(10k-3\right)$$

Use the distributive property to multiply -2B by 10k-3.

$$5Bk-5Ak=70k-21-20Bk+6B$$

Subtract 5Bk from both sides.

$$-5Ak=70k-21-20Bk+6B-5Bk$$

Combine -20Bk and -5Bk to get -25Bk.

$$-5Ak=70k-21-25Bk+6B$$

The equation is in standard form.

$$\left(-5k\right)A=-25Bk+6B+70k-21$$

Divide both sides by -5k.

$$\frac{\left(-5k\right)A}{-5k}=\frac{-25Bk+6B+70k-21}{-5k}$$

Dividing by -5k undoes the multiplication by -5k.

$$A=\frac{-25Bk+6B+70k-21}{-5k}$$

Divide 70k-21-25Bk+6B by -5k.

$$A=5B+\frac{21-6B}{5k}-14$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{21-70k-5Ak}{25k-6}\text{, }&k\neq \frac{6}{25}\text{ and }k\neq \frac{3}{10}\text{ and }k\neq 0\\B\in \mathrm{R}\text{, }&k=\frac{6}{25}\text{ and }A=\frac{7}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5k}{5k}.

$$\frac{B-A}{\frac{2\times 5k}{5k}-\frac{3}{5k}}=7-2B$$

Since \frac{2\times 5k}{5k} and \frac{3}{5k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{B-A}{\frac{2\times 5k-3}{5k}}=7-2B$$

Do the multiplications in 2\times 5k-3.

$$\frac{B-A}{\frac{10k-3}{5k}}=7-2B$$

Divide B-A by \frac{10k-3}{5k} by multiplying B-A by the reciprocal of \frac{10k-3}{5k}.

$$\frac{\left(B-A\right)\times 5k}{10k-3}=7-2B$$

Use the distributive property to multiply B-A by 5.

$$\frac{\left(5B-5A\right)k}{10k-3}=7-2B$$

Use the distributive property to multiply 5B-5A by k.

$$\frac{5Bk-5Ak}{10k-3}=7-2B$$

Add 2B to both sides.

$$\frac{5Bk-5Ak}{10k-3}+2B=7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2B times \frac{10k-3}{10k-3}.

$$\frac{5Bk-5Ak}{10k-3}+\frac{2B\left(10k-3\right)}{10k-3}=7$$

Since \frac{5Bk-5Ak}{10k-3} and \frac{2B\left(10k-3\right)}{10k-3} have the same denominator, add them by adding their numerators.

$$\frac{5Bk-5Ak+2B\left(10k-3\right)}{10k-3}=7$$

Do the multiplications in 5Bk-5Ak+2B\left(10k-3\right).

$$\frac{5Bk-5Ak+20Bk-6B}{10k-3}=7$$

Combine like terms in 5Bk-5Ak+20Bk-6B.

$$\frac{25Bk-5Ak-6B}{10k-3}=7$$

Multiply both sides of the equation by 10k-3.

$$25Bk-5Ak-6B=7\left(10k-3\right)$$

Use the distributive property to multiply 7 by 10k-3.

$$25Bk-5Ak-6B=70k-21$$

Add 5Ak to both sides.

$$25Bk-6B=70k-21+5Ak$$

Combine all terms containing B.

$$\left(25k-6\right)B=70k-21+5Ak$$

The equation is in standard form.

$$\left(25k-6\right)B=5Ak+70k-21$$

Divide both sides by 25k-6.

$$\frac{\left(25k-6\right)B}{25k-6}=\frac{5Ak+70k-21}{25k-6}$$

Dividing by 25k-6 undoes the multiplication by 25k-6.

$$B=\frac{5Ak+70k-21}{25k-6}$$