Solve left(1-mright)left(60+100left(1+1/2xright)right)=100left(1+1/5xright)

$$\left( 1-m \right) \left( 60+100 \left( 1+ \frac{ 1 }{ 2 } x \right) \right) = 100 \left( 1+ \frac{ 1 }{ 5 } x \right)$$

Solve for m

$$m=\frac{3\left(x+2\right)}{5x+16}$$

$$x\neq -\frac{16}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 100 by 1+\frac{1}{2}x.

$$\left(1-m\right)\left(60+100+50x\right)=100\left(1+\frac{1}{5}x\right)$$

Add 60 and 100 to get 160.

$$\left(1-m\right)\left(160+50x\right)=100\left(1+\frac{1}{5}x\right)$$

Use the distributive property to multiply 1-m by 160+50x.

$$160+50x-160m-50mx=100\left(1+\frac{1}{5}x\right)$$

Use the distributive property to multiply 100 by 1+\frac{1}{5}x.

$$160+50x-160m-50mx=100+20x$$

Subtract 160 from both sides.

$$50x-160m-50mx=100+20x-160$$

Subtract 160 from 100 to get -60.

$$50x-160m-50mx=-60+20x$$

Subtract 50x from both sides.

$$-160m-50mx=-60+20x-50x$$

Combine 20x and -50x to get -30x.

$$-160m-50mx=-60-30x$$

Combine all terms containing m.

$$\left(-160-50x\right)m=-60-30x$$

The equation is in standard form.

$$\left(-50x-160\right)m=-30x-60$$

Divide both sides by -160-50x.

$$\frac{\left(-50x-160\right)m}{-50x-160}=\frac{-30x-60}{-50x-160}$$

Dividing by -160-50x undoes the multiplication by -160-50x.

$$m=\frac{-30x-60}{-50x-160}$$

Divide -60-30x by -160-50x.

$$m=\frac{3\left(x+2\right)}{5x+16}$$

Solve for x

$$x=-\frac{2\left(3-8m\right)}{3-5m}$$

$$m\neq \frac{3}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 100 by 1+\frac{1}{2}x.

$$\left(1-m\right)\left(60+100+50x\right)=100\left(1+\frac{1}{5}x\right)$$

Add 60 and 100 to get 160.

$$\left(1-m\right)\left(160+50x\right)=100\left(1+\frac{1}{5}x\right)$$

Use the distributive property to multiply 1-m by 160+50x.

$$160+50x-160m-50xm=100\left(1+\frac{1}{5}x\right)$$

Use the distributive property to multiply 100 by 1+\frac{1}{5}x.

$$160+50x-160m-50xm=100+20x$$

Subtract 20x from both sides.

$$160+50x-160m-50xm-20x=100$$

Combine 50x and -20x to get 30x.

$$160+30x-160m-50xm=100$$

Subtract 160 from both sides.

$$30x-160m-50xm=100-160$$

Subtract 160 from 100 to get -60.

$$30x-160m-50xm=-60$$

Add 160m to both sides.

$$30x-50xm=-60+160m$$

Combine all terms containing x.

$$\left(30-50m\right)x=-60+160m$$

The equation is in standard form.

$$\left(30-50m\right)x=160m-60$$

Divide both sides by -50m+30.

$$\frac{\left(30-50m\right)x}{30-50m}=\frac{160m-60}{30-50m}$$

Dividing by -50m+30 undoes the multiplication by -50m+30.

$$x=\frac{160m-60}{30-50m}$$

Divide -60+160m by -50m+30.

$$x=\frac{2\left(8m-3\right)}{3-5m}$$