Solve (A)1/3x-6=3/4x-8+1

$$( A ) \frac { 1 } { 3 x - 6 } = \frac { 3 } { 4 x - 8 } + 1$$

Solve for A

$$A=3x-\frac{15}{4}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12\left(x-2\right), the least common multiple of 3x-6,4x-8.

$$A\times 4\times 1=3\times 3+12\left(x-2\right)$$

Multiply 4 and 1 to get 4.

$$A\times 4=3\times 3+12\left(x-2\right)$$

Multiply 3 and 3 to get 9.

$$A\times 4=9+12\left(x-2\right)$$

Use the distributive property to multiply 12 by x-2.

$$A\times 4=9+12x-24$$

Subtract 24 from 9 to get -15.

$$A\times 4=-15+12x$$

The equation is in standard form.

$$4A=12x-15$$

Divide both sides by 4.

$$\frac{4A}{4}=\frac{12x-15}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$A=\frac{12x-15}{4}$$

Divide -15+12x by 4.

$$A=3x-\frac{15}{4}$$

Solve for x

$$x=\frac{A}{3}+\frac{5}{4}$$

$$A\neq \frac{9}{4}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 12\left(x-2\right), the least common multiple of 3x-6,4x-8.

$$A\times 4\times 1=3\times 3+12\left(x-2\right)$$

Multiply 4 and 1 to get 4.

$$A\times 4=3\times 3+12\left(x-2\right)$$

Multiply 3 and 3 to get 9.

$$A\times 4=9+12\left(x-2\right)$$

Use the distributive property to multiply 12 by x-2.

$$A\times 4=9+12x-24$$

Subtract 24 from 9 to get -15.

$$A\times 4=-15+12x$$

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

$$-15+12x=A\times 4$$

Add 15 to both sides.

$$12x=A\times 4+15$$

The equation is in standard form.

$$12x=4A+15$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{4A+15}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{4A+15}{12}$$

Divide 4A+15 by 12.

$$x=\frac{A}{3}+\frac{5}{4}$$

Variable x cannot be equal to 2.

$$x=\frac{A}{3}+\frac{5}{4}\text{, }x\neq 2$$