Algebra Examples

$\frac{5}{6} z = - 1 + \frac{3}{2} z - \frac{1}{2} z$

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.

$- 1 + \frac{3}{2} z - \frac{1}{2} z = \frac{5}{6} z$

Step 2

Simplify $- 1 + \frac{3}{2} z - \frac{1}{2} z$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine $\frac{3}{2}$ and $z$ .

$- 1 + \frac{3 z}{2} - \frac{1}{2} z = \frac{5}{6} z$

Step 2.1.2

Combine $z$ and $\frac{1}{2}$ .

$- 1 + \frac{3 z}{2} - \frac{z}{2} = \frac{5}{6} z$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine the numerators over the common denominator.

$- 1 + \frac{3 z - z}{2} = \frac{5}{6} z$

Step 2.2.2

Subtract $z$ from $3 z$ .

$- 1 + \frac{2 z}{2} = \frac{5}{6} z$

Step 2.2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.3.1

Cancel the common factor.

$- 1 + \frac{2 z}{2} = \frac{5}{6} z$

Step 2.2.3.2

Divide $z$ by $1$ .

$- 1 + z = \frac{5}{6} z$

Step 3

Combine $\frac{5}{6}$ and $z$ .

$- 1 + z = \frac{5 z}{6}$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $\frac{5 z}{6}$ from both sides of the equation.

$- 1 + z - \frac{5 z}{6} = 0$

Step 4.2

To write $z$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- 1 + z \cdot \frac{6}{6} - \frac{5 z}{6} = 0$

Step 4.3

Combine $z$ and $\frac{6}{6}$ .

$- 1 + \frac{z \cdot 6}{6} - \frac{5 z}{6} = 0$

Step 4.4

Combine the numerators over the common denominator.

$- 1 + \frac{z \cdot 6 - 5 z}{6} = 0$

Step 4.5

Subtract $5 z$ from $z \cdot 6$ .

Tap for more steps...

Step 4.5.1

Reorder $z$ and $6$ .

$- 1 + \frac{6 \cdot z - 5 z}{6} = 0$

Step 4.5.2

Subtract $5 z$ from $6 \cdot z$ .

$- 1 + \frac{z}{6} = 0$

Step 5

Add $1$ to both sides of the equation.

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

Step 6

Multiply both sides of the equation by $6$ .

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

Step 7

Simplify both sides of the equation.

Tap for more steps...

Step 7.1

Simplify the left side.

Tap for more steps...

Step 7.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 7.1.1.1

Cancel the common factor.

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

Step 7.1.1.2

Rewrite the expression.

$z = 6 \cdot 1$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Multiply $6$ by $1$ .

$z = 6$