Basic Math Examples

$\frac{2}{3} z + 10 = \frac{1}{3} z$

Step 1

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

$\frac{2 z}{3} + 10 = \frac{1}{3} z$

Step 2

Combine $\frac{1}{3}$ and $z$ .

$\frac{2 z}{3} + 10 = \frac{z}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{z}{3}$ from both sides of the equation.

$\frac{2 z}{3} + 10 - \frac{z}{3} = 0$

Step 3.2

Combine the numerators over the common denominator.

$10 + \frac{2 z - z}{3} = 0$

Step 3.3

Subtract $z$ from $2 z$ .

$10 + \frac{z}{3} = 0$

Step 4

Subtract $10$ from both sides of the equation.

$\frac{z}{3} = - 10$

Step 5

Multiply both sides of the equation by $3$ .

$3 \frac{z}{3} = 3 \cdot - 10$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1

Cancel the common factor.

$3 \frac{z}{3} = 3 \cdot - 10$

Step 6.1.1.2

Rewrite the expression.

$z = 3 \cdot - 10$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $3$ by $- 10$ .

$z = - 30$