Solve m(2x-3)/5+(4x-1)/10=1

$$m \frac { ( 2 x - 3 ) } { 5 } + \frac { ( 4 x - 1 ) } { 10 } = 1$$

Solve for m

$$m=-\frac{4x-11}{2\left(2x-3\right)}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10.

$$2m\left(2x-3\right)+4x-1=10$$

Use the distributive property to multiply 2m by 2x-3.

$$4mx-6m+4x-1=10$$

Subtract 4x from both sides.

$$4mx-6m-1=10-4x$$

Add 1 to both sides.

$$4mx-6m=10-4x+1$$

Add 10 and 1 to get 11.

$$4mx-6m=11-4x$$

Combine all terms containing m.

$$\left(4x-6\right)m=11-4x$$

Divide both sides by 4x-6.

$$\frac{\left(4x-6\right)m}{4x-6}=\frac{11-4x}{4x-6}$$

Dividing by 4x-6 undoes the multiplication by 4x-6.

$$m=\frac{11-4x}{4x-6}$$

Divide 11-4x by 4x-6.

$$m=\frac{11-4x}{2\left(2x-3\right)}$$

Solve for x

$$x=\frac{6m+11}{4\left(m+1\right)}$$

$$m\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10.

$$2m\left(2x-3\right)+4x-1=10$$

Use the distributive property to multiply 2m by 2x-3.

$$4xm-6m+4x-1=10$$

Add 6m to both sides.

$$4xm+4x-1=10+6m$$

Add 1 to both sides.

$$4xm+4x=10+6m+1$$

Add 10 and 1 to get 11.

$$4xm+4x=11+6m$$

Combine all terms containing x.

$$\left(4m+4\right)x=11+6m$$

The equation is in standard form.

$$\left(4m+4\right)x=6m+11$$

Divide both sides by 4m+4.

$$\frac{\left(4m+4\right)x}{4m+4}=\frac{6m+11}{4m+4}$$

Dividing by 4m+4 undoes the multiplication by 4m+4.

$$x=\frac{6m+11}{4m+4}$$

Divide 11+6m by 4m+4.

$$x=\frac{6m+11}{4\left(m+1\right)}$$