Solve 3x=(2x-1)(m+4)

$$3 x = ( 2 x - 1 ) ( m + 4 )$$

Solve for m

$$m=-\frac{4-5x}{1-2x}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by m+4.

$$3x=2xm+8x-m-4$$

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

$$2xm+8x-m-4=3x$$

Subtract 8x from both sides.

$$2xm-m-4=3x-8x$$

Combine 3x and -8x to get -5x.

$$2xm-m-4=-5x$$

Add 4 to both sides.

$$2xm-m=-5x+4$$

Combine all terms containing m.

$$\left(2x-1\right)m=-5x+4$$

The equation is in standard form.

$$\left(2x-1\right)m=4-5x$$

Divide both sides by 2x-1.

$$\frac{\left(2x-1\right)m}{2x-1}=\frac{4-5x}{2x-1}$$

Dividing by 2x-1 undoes the multiplication by 2x-1.

$$m=\frac{4-5x}{2x-1}$$

Solve for x

$$x=\frac{m+4}{2m+5}$$

$$m\neq -\frac{5}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by m+4.

$$3x=2xm+8x-m-4$$

Subtract 2xm from both sides.

$$3x-2xm=8x-m-4$$

Subtract 8x from both sides.

$$3x-2xm-8x=-m-4$$

Combine 3x and -8x to get -5x.

$$-5x-2xm=-m-4$$

Combine all terms containing x.

$$\left(-5-2m\right)x=-m-4$$

The equation is in standard form.

$$\left(-2m-5\right)x=-m-4$$

Divide both sides by -5-2m.

$$\frac{\left(-2m-5\right)x}{-2m-5}=\frac{-m-4}{-2m-5}$$

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

$$x=\frac{-m-4}{-2m-5}$$

Divide -m-4 by -5-2m.

$$x=\frac{m+4}{2m+5}$$