Basic Math Examples

$- \frac{2}{3} a + \frac{3}{7} = \frac{1}{2}$

Step 1

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{2}{3} a + \frac{3}{7} - \frac{1}{2} = 0$

Step 2

Simplify $- \frac{2}{3} a + \frac{3}{7} - \frac{1}{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$- \frac{a \cdot 2}{3} + \frac{3}{7} - \frac{1}{2} = 0$

Step 2.1.2

Move $2$ to the left of $a$ .

$- \frac{2 a}{3} + \frac{3}{7} - \frac{1}{2} = 0$

Step 2.2

To write $\frac{3}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2 a}{3} + \frac{3}{7} \cdot \frac{2}{2} - \frac{1}{2} = 0$

Step 2.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{2 a}{3} + \frac{3}{7} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{7}{7} = 0$

Step 2.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{3}{7}$ by $\frac{2}{2}$ .

$- \frac{2 a}{3} + \frac{3 \cdot 2}{7 \cdot 2} - \frac{1}{2} \cdot \frac{7}{7} = 0$

Step 2.4.2

Multiply $7$ by $2$ .

$- \frac{2 a}{3} + \frac{3 \cdot 2}{14} - \frac{1}{2} \cdot \frac{7}{7} = 0$

Step 2.4.3

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$- \frac{2 a}{3} + \frac{3 \cdot 2}{14} - \frac{7}{2 \cdot 7} = 0$

Step 2.4.4

Multiply $2$ by $7$ .

$- \frac{2 a}{3} + \frac{3 \cdot 2}{14} - \frac{7}{14} = 0$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{2 a}{3} + \frac{3 \cdot 2 - 7}{14} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $2$ .

$- \frac{2 a}{3} + \frac{6 - 7}{14} = 0$

Step 2.6.2

Subtract $7$ from $6$ .

$- \frac{2 a}{3} + \frac{- 1}{14} = 0$

Step 2.7

Move the negative in front of the fraction.

$- \frac{2 a}{3} - \frac{1}{14} = 0$

Step 3

Factor the left side.

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Step 3.1

Factor $- 1$ out of $- \frac{2 a}{3} - \frac{1}{14}$ .

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Step 3.1.1

Factor $- 1$ out of $- \frac{2 a}{3}$ .

$- (\frac{2 a}{3}) - \frac{1}{14} = 0$

Step 3.1.2

Factor $- 1$ out of $- \frac{1}{14}$ .

$- (\frac{2 a}{3}) - (\frac{1}{14}) = 0$

Step 3.1.3

Factor $- 1$ out of $- (\frac{2 a}{3}) - (\frac{1}{14})$ .

$- (\frac{2 a}{3} + \frac{1}{14}) = 0$

Step 3.2

To write $\frac{2 a}{3}$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$- (\frac{2 a}{3} \cdot \frac{14}{14} + \frac{1}{14}) = 0$

Step 3.3

To write $\frac{1}{14}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- (\frac{2 a}{3} \cdot \frac{14}{14} + \frac{1}{14} \cdot \frac{3}{3}) = 0$

Step 3.4

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{2 a}{3}$ by $\frac{14}{14}$ .

$- (\frac{2 a \cdot 14}{3 \cdot 14} + \frac{1}{14} \cdot \frac{3}{3}) = 0$

Step 3.4.2

Multiply $3$ by $14$ .

$- (\frac{2 a \cdot 14}{42} + \frac{1}{14} \cdot \frac{3}{3}) = 0$

Step 3.4.3

Multiply $\frac{1}{14}$ by $\frac{3}{3}$ .

$- (\frac{2 a \cdot 14}{42} + \frac{3}{14 \cdot 3}) = 0$

Step 3.4.4

Multiply $14$ by $3$ .

$- (\frac{2 a \cdot 14}{42} + \frac{3}{42}) = 0$

Step 3.5

Combine the numerators over the common denominator.

$- \frac{2 a \cdot 14 + 3}{42} = 0$

Step 3.6

Multiply $14$ by $2$ .

$- \frac{28 a + 3}{42} = 0$