Pre-Algebra Examples

$\frac{3 (2 - z)}{2} = - z$

Step 1

Multiply both sides by $2$ .

$\frac{3 (2 - z)}{2} \cdot 2 = - z \cdot 2$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{3 (2 - z)}{2} \cdot 2$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1.1

Cancel the common factor.

$\frac{3 (2 - z)}{2} \cdot 2 = - z \cdot 2$

Step 2.1.1.1.2

Rewrite the expression.

$3 (2 - z) = - z \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$3 \cdot 2 + 3 (- z) = - z \cdot 2$

Step 2.1.1.3

Simplify the expression.

Tap for more steps...

Step 2.1.1.3.1

Multiply $3$ by $2$ .

$6 + 3 (- z) = - z \cdot 2$

Step 2.1.1.3.2

Multiply $- 1$ by $3$ .

$6 - 3 z = - z \cdot 2$

Step 2.1.1.3.3

Reorder $6$ and $- 3 z$ .

$- 3 z + 6 = - z \cdot 2$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $- 1$ .

$- 3 z + 6 = - 2 z$

Step 3

Solve for $z$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $2 z$ to both sides of the equation.

$- 3 z + 6 + 2 z = 0$

Step 3.1.2

Add $- 3 z$ and $2 z$ .

$- z + 6 = 0$

Step 3.2

Subtract $6$ from both sides of the equation.

$- z = - 6$

Step 3.3

Divide each term in $- z = - 6$ by $- 1$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- z = - 6$ by $- 1$ .

$\frac{- z}{- 1} = \frac{- 6}{- 1}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{- 6}{- 1}$

Step 3.3.2.2

Divide $z$ by $1$ .

$z = \frac{- 6}{- 1}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $- 6$ by $- 1$ .

$z = 6$