Solve 1.1x-0.56=-0.25left(-0.2x+1.92right)+z

$$1.1x-0.56 = -0.25 \left( -0.2x+1.92 \right) +z$$

Solve for x

$$x=\frac{20z}{21}+\frac{8}{105}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -0.25 by -0.2x+1.92.

$$1.1x-0.56=0.05x-0.48+z$$

Subtract 0.05x from both sides.

$$1.1x-0.56-0.05x=-0.48+z$$

Combine 1.1x and -0.05x to get 1.05x.

$$1.05x-0.56=-0.48+z$$

Add 0.56 to both sides.

$$1.05x=-0.48+z+0.56$$

Add -0.48 and 0.56 to get 0.08.

$$1.05x=0.08+z$$

The equation is in standard form.

$$1.05x=z+0.08$$

Divide both sides of the equation by 1.05, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{1.05x}{1.05}=\frac{z+0.08}{1.05}$$

Dividing by 1.05 undoes the multiplication by 1.05.

$$x=\frac{z+0.08}{1.05}$$

Divide 0.08+z by 1.05 by multiplying 0.08+z by the reciprocal of 1.05.

$$x=\frac{20z}{21}+\frac{8}{105}$$

Solve for z

$$z=\frac{21x}{20}-0.08$$

Solution Steps

Use the distributive property to multiply -0.25 by -0.2x+1.92.

$$1.1x-0.56=0.05x-0.48+z$$

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

$$0.05x-0.48+z=1.1x-0.56$$

Subtract 0.05x from both sides.

$$-0.48+z=1.1x-0.56-0.05x$$

Combine 1.1x and -0.05x to get 1.05x.

$$-0.48+z=1.05x-0.56$$

Add 0.48 to both sides.

$$z=1.05x-0.56+0.48$$

Add -0.56 and 0.48 to get -0.08.

$$z=1.05x-0.08$$