Solve A=3x+2/2(x-1)-3(2x+1)

$$A = \frac { 3 x + 2 } { 2 ( x - 1 ) - 3 ( 2 x + 1 ) }$$

Solve for x

$$x=-\frac{5A+2}{4A+3}$$

$$A\neq -\frac{3}{4}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{5}{4} since division by zero is not defined. Multiply both sides of the equation by -4x-5.

$$A\left(-4x-5\right)=3x+2$$

Use the distributive property to multiply A by -4x-5.

$$-4Ax-5A=3x+2$$

Subtract 3x from both sides.

$$-4Ax-5A-3x=2$$

Add 5A to both sides.

$$-4Ax-3x=2+5A$$

Combine all terms containing x.

$$\left(-4A-3\right)x=2+5A$$

The equation is in standard form.

$$\left(-4A-3\right)x=5A+2$$

Divide both sides by -4A-3.

$$\frac{\left(-4A-3\right)x}{-4A-3}=\frac{5A+2}{-4A-3}$$

Dividing by -4A-3 undoes the multiplication by -4A-3.

$$x=\frac{5A+2}{-4A-3}$$

Divide 5A+2 by -4A-3.

$$x=-\frac{5A+2}{4A+3}$$

Variable x cannot be equal to -\frac{5}{4}.

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

Solve for A

$$A=-\frac{3x+2}{4x+5}$$

$$x\neq -\frac{5}{4}$$