Algebra Examples

$- 2 + \frac{2}{3} w = 10$

Step 1

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

$- 2 + \frac{2 w}{3} = 10$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

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

Step 2.2

Add $10$ and $2$ .

$\frac{2 w}{3} = 12$

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 w}{3} = \frac{3}{2} \cdot 12$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 w}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 w}{3} = \frac{3}{2} \cdot 12$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 w) = \frac{3}{2} \cdot 12$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 w$ .

$\frac{1}{2} (2 (w)) = \frac{3}{2} \cdot 12$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 w) = \frac{3}{2} \cdot 12$

Step 4.1.1.2.3

Rewrite the expression.

$w = \frac{3}{2} \cdot 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} \cdot 12$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $12$ .

$w = \frac{3}{2} \cdot (2 (6))$

Step 4.2.1.1.2

Cancel the common factor.

$w = \frac{3}{2} \cdot (2 \cdot 6)$

Step 4.2.1.1.3

Rewrite the expression.

$w = 3 \cdot 6$

Step 4.2.1.2

Multiply $3$ by $6$ .

$w = 18$