Solve a5+15/b5+15-1=30

$$\frac{ a5+15 }{ b5+15 } -1 = 30$$

Solve for a_5

$$a_{5}=31b_{5}+450$$

$$b_{5}\neq -15$$

Solution Steps

Multiply both sides of the equation by b_{5}+15.

$$a_{5}+15+\left(b_{5}+15\right)\left(-1\right)=30\left(b_{5}+15\right)$$

Use the distributive property to multiply b_{5}+15 by -1.

$$a_{5}+15-b_{5}-15=30\left(b_{5}+15\right)$$

Subtract 15 from 15 to get 0.

$$a_{5}-b_{5}=30\left(b_{5}+15\right)$$

Use the distributive property to multiply 30 by b_{5}+15.

$$a_{5}-b_{5}=30b_{5}+450$$

Add b_{5} to both sides.

$$a_{5}=30b_{5}+450+b_{5}$$

Combine 30b_{5} and b_{5} to get 31b_{5}.

$$a_{5}=31b_{5}+450$$

Solve for b_5

$$b_{5}=\frac{a_{5}-450}{31}$$

$$a_{5}\neq -15$$

Steps for Solving Linear Equation

Variable b_{5} cannot be equal to -15 since division by zero is not defined. Multiply both sides of the equation by b_{5}+15.

$$a_{5}+15+\left(b_{5}+15\right)\left(-1\right)=30\left(b_{5}+15\right)$$

Use the distributive property to multiply b_{5}+15 by -1.

$$a_{5}+15-b_{5}-15=30\left(b_{5}+15\right)$$

Subtract 15 from 15 to get 0.

$$a_{5}-b_{5}=30\left(b_{5}+15\right)$$

Use the distributive property to multiply 30 by b_{5}+15.

$$a_{5}-b_{5}=30b_{5}+450$$

Subtract 30b_{5} from both sides.

$$a_{5}-b_{5}-30b_{5}=450$$

Combine -b_{5} and -30b_{5} to get -31b_{5}.

$$a_{5}-31b_{5}=450$$

Subtract a_{5} from both sides.

$$-31b_{5}=450-a_{5}$$

Divide both sides by -31.

$$\frac{-31b_{5}}{-31}=\frac{450-a_{5}}{-31}$$

Dividing by -31 undoes the multiplication by -31.

$$b_{5}=\frac{450-a_{5}}{-31}$$

Divide 450-a_{5} by -31.

$$b_{5}=\frac{a_{5}-450}{31}$$

Variable b_{5} cannot be equal to -15.

$$b_{5}=\frac{a_{5}-450}{31}\text{, }b_{5}\neq -15$$