Basic Math Examples

$\frac{1}{3} \cdot (9 z - 6) = 2 z + 3$

Step 1

Simplify $\frac{1}{3} \cdot (9 z - 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (9 z - 6) = 2 z + 3$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (9 z - 6) = 2 z + 3$

Step 1.3

Apply the distributive property.

$\frac{1}{3} (9 z) + \frac{1}{3} \cdot - 6 = 2 z + 3$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9 z$ .

$\frac{1}{3} (3 (3 z)) + \frac{1}{3} \cdot - 6 = 2 z + 3$

Step 1.4.2

Cancel the common factor.

$\frac{1}{3} (3 (3 z)) + \frac{1}{3} \cdot - 6 = 2 z + 3$

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 6$ .

$3 z + \frac{1}{3} \cdot (3 (- 2)) = 2 z + 3$

Step 1.5.2

Cancel the common factor.

$3 z + \frac{1}{3} \cdot (3 \cdot - 2) = 2 z + 3$

Step 1.5.3

Rewrite the expression.

$3 z - 2 = 2 z + 3$

Step 2

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

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Step 2.1

Subtract $2 z$ from both sides of the equation.

$3 z - 2 - 2 z = 3$

Step 2.2

Subtract $2 z$ from $3 z$ .

$z - 2 = 3$

Step 3

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

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Step 3.1

Add $2$ to both sides of the equation.

$z = 3 + 2$

Step 3.2

Add $3$ and $2$ .

$z = 5$