Algebra Examples

$\frac{2}{3} (9 h - 3) = 3 h$

Step 1

Simplify $\frac{2}{3} \cdot (9 h - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (9 h - 3) = 3 h$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (9 h - 3) = 3 h$

Step 1.3

Apply the distributive property.

$\frac{2}{3} (9 h) + \frac{2}{3} \cdot - 3 = 3 h$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9 h$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Multiply $3$ by $2$ .

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

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Factor $3$ out of $- 3$ .

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

Step 1.6.2

Cancel the common factor.

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

Step 1.6.3

Rewrite the expression.

$6 h + 2 \cdot - 1 = 3 h$

Step 1.7

Multiply $2$ by $- 1$ .

$6 h - 2 = 3 h$

Step 2

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

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Step 2.1

Subtract $3 h$ from both sides of the equation.

$6 h - 2 - 3 h = 0$

Step 2.2

Subtract $3 h$ from $6 h$ .

$3 h - 2 = 0$

Step 3

Add $2$ to both sides of the equation.

$3 h = 2$

Step 4

Divide each term in $3 h = 2$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 h = 2$ by $3$ .

$\frac{3 h}{3} = \frac{2}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 h}{3} = \frac{2}{3}$

Step 4.2.1.2

Divide $h$ by $1$ .

$h = \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = \frac{2}{3}$

Decimal Form:

$h = 0.\overline{6}$