Solve a-1/2+5/2b-3=10

$$\frac { a - 1 } { 2 } + \frac { 5 } { 2 b - 3 } = 10$$

Solve for a

$$a=-\frac{73-42b}{2b-3}$$

$$b\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(2b-3\right), the least common multiple of 2,2b-3.

$$\left(2b-3\right)\left(a-1\right)+2\times 5=20\left(2b-3\right)$$

Use the distributive property to multiply 2b-3 by a-1.

$$2ba-2b-3a+3+2\times 5=20\left(2b-3\right)$$

Multiply 2 and 5 to get 10.

$$2ba-2b-3a+3+10=20\left(2b-3\right)$$

Add 3 and 10 to get 13.

$$2ba-2b-3a+13=20\left(2b-3\right)$$

Use the distributive property to multiply 20 by 2b-3.

$$2ba-2b-3a+13=40b-60$$

Add 2b to both sides.

$$2ba-3a+13=40b-60+2b$$

Combine 40b and 2b to get 42b.

$$2ba-3a+13=42b-60$$

Subtract 13 from both sides.

$$2ba-3a=42b-60-13$$

Subtract 13 from -60 to get -73.

$$2ba-3a=42b-73$$

Combine all terms containing a.

$$\left(2b-3\right)a=42b-73$$

Divide both sides by 2b-3.

$$\frac{\left(2b-3\right)a}{2b-3}=\frac{42b-73}{2b-3}$$

Dividing by 2b-3 undoes the multiplication by 2b-3.

$$a=\frac{42b-73}{2b-3}$$

Solve for b

$$b=-\frac{73-3a}{2\left(a-21\right)}$$

$$a\neq 21$$

Steps for Solving Linear Equation

Variable b cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2\left(2b-3\right), the least common multiple of 2,2b-3.

$$\left(2b-3\right)\left(a-1\right)+2\times 5=20\left(2b-3\right)$$

Use the distributive property to multiply 2b-3 by a-1.

$$2ba-2b-3a+3+2\times 5=20\left(2b-3\right)$$

Multiply 2 and 5 to get 10.

$$2ba-2b-3a+3+10=20\left(2b-3\right)$$

Add 3 and 10 to get 13.

$$2ba-2b-3a+13=20\left(2b-3\right)$$

Use the distributive property to multiply 20 by 2b-3.

$$2ba-2b-3a+13=40b-60$$

Subtract 40b from both sides.

$$2ba-2b-3a+13-40b=-60$$

Combine -2b and -40b to get -42b.

$$2ba-42b-3a+13=-60$$

Add 3a to both sides.

$$2ba-42b+13=-60+3a$$

Subtract 13 from both sides.

$$2ba-42b=-60+3a-13$$

Subtract 13 from -60 to get -73.

$$2ba-42b=-73+3a$$

Combine all terms containing b.

$$\left(2a-42\right)b=-73+3a$$

The equation is in standard form.

$$\left(2a-42\right)b=3a-73$$

Divide both sides by -42+2a.

$$\frac{\left(2a-42\right)b}{2a-42}=\frac{3a-73}{2a-42}$$

Dividing by -42+2a undoes the multiplication by -42+2a.

$$b=\frac{3a-73}{2a-42}$$

Divide -73+3a by -42+2a.

$$b=\frac{3a-73}{2\left(a-21\right)}$$

Variable b cannot be equal to \frac{3}{2}.

$$b=\frac{3a-73}{2\left(a-21\right)}\text{, }b\neq \frac{3}{2}$$