Algebra Examples

$\frac{1}{2} h - 3 = \frac{3}{2} - 3 h$

Step 1

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

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

Step 2

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

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Step 2.1

Add $3 h$ to both sides of the equation.

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

Step 2.2

To write $3 h$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $h$ out of $h + 3 h \cdot 2$ .

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Step 2.5.1.1.1

Raise $h$ to the power of $1$ .

$\frac{h^{1} + 3 h \cdot 2}{2} - 3 = \frac{3}{2}$

Step 2.5.1.1.2

Factor $h$ out of $h^{1}$ .

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

Step 2.5.1.1.3

Factor $h$ out of $3 h \cdot 2$ .

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

Step 2.5.1.1.4

Factor $h$ out of $h \cdot 1 + h (3 \cdot 2)$ .

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

Step 2.5.1.2

Multiply $3$ by $2$ .

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

Step 2.5.1.3

Add $1$ and $6$ .

$\frac{h \cdot 7}{2} - 3 = \frac{3}{2}$

Step 2.5.2

Move $7$ to the left of $h$ .

$\frac{7 h}{2} - 3 = \frac{3}{2}$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$\frac{7 h}{2} = \frac{3}{2} + 3$

Step 3.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 h}{2} = \frac{3}{2} + 3 \cdot \frac{2}{2}$

Step 3.3

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

$\frac{7 h}{2} = \frac{3}{2} + \frac{3 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{7 h}{2} = \frac{3 + 3 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $2$ .

$\frac{7 h}{2} = \frac{3 + 6}{2}$

Step 3.5.2

Add $3$ and $6$ .

$\frac{7 h}{2} = \frac{9}{2}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 h = 9$

Step 5

Divide each term in $7 h = 9$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 h = 9$ by $7$ .

$\frac{7 h}{7} = \frac{9}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 h}{7} = \frac{9}{7}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{9}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$h = \frac{9}{7}$

Decimal Form:

$h = 1.\overline{285714}$

Mixed Number Form:

$h = 1 \frac{2}{7}$