Solve A=2x-6/5x-15

$$A = \frac { 2 x - 6 } { 5 x - 15 }$$

Solve for A

$$A=\frac{2}{5}=0.4$$

$$x\neq 3$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{2x-6}{5x-15}.

$$A=\frac{2\left(x-3\right)}{5\left(x-3\right)}$$

Cancel out x-3 in both numerator and denominator.

$$A=\frac{2}{5}$$

Solve for x

$$x\neq 3$$

$$A=\frac{2}{5}\text{ and }x\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 5\left(x-3\right).

$$A\times 5\left(x-3\right)=2x-6$$

Use the distributive property to multiply A\times 5 by x-3.

$$5Ax-3A\times 5=2x-6$$

Multiply -3 and 5 to get -15.

$$5Ax-15A=2x-6$$

Subtract 2x from both sides.

$$5Ax-15A-2x=-6$$

Add 15A to both sides.

$$5Ax-2x=-6+15A$$

Combine all terms containing x.

$$\left(5A-2\right)x=-6+15A$$

The equation is in standard form.

$$\left(5A-2\right)x=15A-6$$

Divide both sides by 5A-2.

$$\frac{\left(5A-2\right)x}{5A-2}=\frac{15A-6}{5A-2}$$

Dividing by 5A-2 undoes the multiplication by 5A-2.

$$x=\frac{15A-6}{5A-2}$$

Divide -6+15A by 5A-2.

$$x=3$$

Variable x cannot be equal to 3.

$$x\in \emptyset$$