Solve for z 0.4+0.5z=0.6z+0.1z+2

$0.4 + 0.5 z = 0.6 z + 0.1 z + 2$

Step 1

Since $z$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$0.6 z + 0.1 z + 2 = 0.4 + 0.5 z$

Step 2

Add $0.6 z$ and $0.1 z$ .

$0.7 z + 2 = 0.4 + 0.5 z$

Step 3

Move all terms containing $z$ to the left side of the equation.

Subtract $0.5 z$ from both sides of the equation.

$0.7 z + 2 - 0.5 z = 0.4$

Subtract $0.5 z$ from $0.7 z$ .

$0.2 z + 2 = 0.4$

Step 4

Move all terms not containing $z$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$0.2 z = 0.4 - 2$

Subtract $2$ from $0.4$ .

$0.2 z = - 1.6$

Step 5

Divide each term in $0.2 z = - 1.6$ by $0.2$ and simplify.

Divide each term in $0.2 z = - 1.6$ by $0.2$ .

$\frac{0.2 z}{0.2} = \frac{- 1.6}{0.2}$

Simplify the left side.

Cancel the common factor of $0.2$ .

Cancel the common factor.

$\frac{0.2 z}{0.2} = \frac{- 1.6}{0.2}$

Divide $z$ by $1$ .

$z = \frac{- 1.6}{0.2}$

Simplify the right side.

Divide $- 1.6$ by $0.2$ .

$z = - 8$