Basic Math Examples

$\frac{3 a}{2} + \frac{4 a + 7}{5} = 6$

Step 1

Simplify $\frac{3 a}{2} + \frac{4 a + 7}{5}$ .

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Step 1.1

To write $\frac{3 a}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 a}{2} \cdot \frac{5}{5} + \frac{4 a + 7}{5} = 6$

Step 1.2

To write $\frac{4 a + 7}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 a}{2} \cdot \frac{5}{5} + \frac{4 a + 7}{5} \cdot \frac{2}{2} = 6$

Step 1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 a}{2}$ by $\frac{5}{5}$ .

$\frac{3 a \cdot 5}{2 \cdot 5} + \frac{4 a + 7}{5} \cdot \frac{2}{2} = 6$

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{3 a \cdot 5}{10} + \frac{4 a + 7}{5} \cdot \frac{2}{2} = 6$

Step 1.3.3

Multiply $\frac{4 a + 7}{5}$ by $\frac{2}{2}$ .

$\frac{3 a \cdot 5}{10} + \frac{(4 a + 7) \cdot 2}{5 \cdot 2} = 6$

Step 1.3.4

Multiply $5$ by $2$ .

$\frac{3 a \cdot 5}{10} + \frac{(4 a + 7) \cdot 2}{10} = 6$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 a \cdot 5 + (4 a + 7) \cdot 2}{10} = 6$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $3$ .

$\frac{15 a + (4 a + 7) \cdot 2}{10} = 6$

Step 1.5.2

Apply the distributive property.

$\frac{15 a + 4 a \cdot 2 + 7 \cdot 2}{10} = 6$

Step 1.5.3

Multiply $2$ by $4$ .

$\frac{15 a + 8 a + 7 \cdot 2}{10} = 6$

Step 1.5.4

Multiply $7$ by $2$ .

$\frac{15 a + 8 a + 14}{10} = 6$

Step 1.5.5

Add $15 a$ and $8 a$ .

$\frac{23 a + 14}{10} = 6$

Step 2

Multiply both sides by $10$ .

$\frac{23 a + 14}{10} \cdot 10 = 6 \cdot 10$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{23 a + 14}{10} \cdot 10 = 6 \cdot 10$

Step 3.1.1.2

Rewrite the expression.

$23 a + 14 = 6 \cdot 10$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $6$ by $10$ .

$23 a + 14 = 60$

Step 4

Solve for $a$ .

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Step 4.1

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

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Step 4.1.1

Subtract $14$ from both sides of the equation.

$23 a = 60 - 14$

Step 4.1.2

Subtract $14$ from $60$ .

$23 a = 46$

Step 4.2

Divide each term in $23 a = 46$ by $23$ and simplify.

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Step 4.2.1

Divide each term in $23 a = 46$ by $23$ .

$\frac{23 a}{23} = \frac{46}{23}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $23$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{23 a}{23} = \frac{46}{23}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{46}{23}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $46$ by $23$ .

$a = 2$