Basic Math Examples

$\frac{a + 5}{3} = 7 + 3 a$

Step 1

Multiply both sides by $3$ .

$\frac{a + 5}{3} \cdot 3 = (7 + 3 a) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{a + 5}{3} \cdot 3 = (7 + 3 a) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$a + 5 = (7 + 3 a) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(7 + 3 a) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$a + 5 = 7 \cdot 3 + 3 a \cdot 3$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $7$ by $3$ .

$a + 5 = 21 + 3 a \cdot 3$

Step 2.2.1.2.2

Multiply $3$ by $3$ .

$a + 5 = 21 + 9 a$

Step 2.2.1.2.3

Reorder $21$ and $9 a$ .

$a + 5 = 9 a + 21$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

Subtract $9 a$ from both sides of the equation.

$a + 5 - 9 a = 21$

Step 3.1.2

Subtract $9 a$ from $a$ .

$- 8 a + 5 = 21$

Step 3.2

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

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$- 8 a = 21 - 5$

Step 3.2.2

Subtract $5$ from $21$ .

$- 8 a = 16$

Step 3.3

Divide each term in $- 8 a = 16$ by $- 8$ and simplify.

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Step 3.3.1

Divide each term in $- 8 a = 16$ by $- 8$ .

$\frac{- 8 a}{- 8} = \frac{16}{- 8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 8 a}{- 8} = \frac{16}{- 8}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{16}{- 8}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $16$ by $- 8$ .

$a = - 2$