Solve 2m(2x-1)+5=m(x+4)

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

Solve for m

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

$$x\neq 2$$

Steps for Solving Linear Equation

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

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

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

$$4mx-2m+5=mx+4m$$

Subtract mx from both sides.

$$4mx-2m+5-mx=4m$$

Combine 4mx and -mx to get 3mx.

$$3mx-2m+5=4m$$

Subtract 4m from both sides.

$$3mx-2m+5-4m=0$$

Combine -2m and -4m to get -6m.

$$3mx-6m+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$3mx-6m=-5$$

Combine all terms containing m.

$$\left(3x-6\right)m=-5$$

Divide both sides by 3x-6.

$$\frac{\left(3x-6\right)m}{3x-6}=-\frac{5}{3x-6}$$

Dividing by 3x-6 undoes the multiplication by 3x-6.

$$m=-\frac{5}{3x-6}$$

Divide -5 by 3x-6.

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

Solve for x

$$x=2-\frac{5}{3m}$$

$$m\neq 0$$

Steps for Solving Linear Equation

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

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

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

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

Subtract mx from both sides.

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

Combine 4xm and -mx to get 3xm.

$$3xm-2m+5=4m$$

Add 2m to both sides.

$$3xm+5=4m+2m$$

Combine 4m and 2m to get 6m.

$$3xm+5=6m$$

Subtract 5 from both sides.

$$3xm=6m-5$$

The equation is in standard form.

$$3mx=6m-5$$

Divide both sides by 3m.

$$\frac{3mx}{3m}=\frac{6m-5}{3m}$$

Dividing by 3m undoes the multiplication by 3m.

$$x=\frac{6m-5}{3m}$$

Divide 6m-5 by 3m.

$$x=2-\frac{5}{3m}$$