Pre-Algebra Examples

$a + 2 = \frac{a}{7}$

Step 1

Multiply both sides by $7$ .

$(a + 2) \cdot 7 = \frac{a}{7} \cdot 7$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(a + 2) \cdot 7$ .

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Step 2.1.1.1

Apply the distributive property.

$a \cdot 7 + 2 \cdot 7 = \frac{a}{7} \cdot 7$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

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

$7 \cdot a + 2 \cdot 7 = \frac{a}{7} \cdot 7$

Step 2.1.1.2.2

Multiply $2$ by $7$ .

$7 a + 14 = \frac{a}{7} \cdot 7$

$7 a + 14 = \frac{a}{7} \cdot 7$

$7 a + 14 = \frac{a}{7} \cdot 7$

$7 a + 14 = \frac{a}{7} \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$7 a + 14 = \frac{a}{7} \cdot 7$

Step 2.2.1.2

Rewrite the expression.

$7 a + 14 = a$

$7 a + 14 = a$

$7 a + 14 = a$

$7 a + 14 = a$

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 $a$ from both sides of the equation.

$7 a + 14 - a = 0$

Step 3.1.2

Subtract $a$ from $7 a$ .

$6 a + 14 = 0$

$6 a + 14 = 0$

Step 3.2

Subtract $14$ from both sides of the equation.

$6 a = - 14$

Step 3.3

Divide each term in $6 a = - 14$ by $6$ and simplify.

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Step 3.3.1

Divide each term in $6 a = - 14$ by $6$ .

$\frac{6 a}{6} = \frac{- 14}{6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 14}{6}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 14}{6}$

$a = \frac{- 14}{6}$

$a = \frac{- 14}{6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $- 14$ and $6$ .

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Step 3.3.3.1.1

Factor $2$ out of $- 14$ .

$a = \frac{2 (- 7)}{6}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $2$ out of $6$ .

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

Step 3.3.3.1.2.2

Cancel the common factor.

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

Step 3.3.3.1.2.3

Rewrite the expression.

$a = \frac{- 7}{3}$

$a = \frac{- 7}{3}$

$a = \frac{- 7}{3}$

Step 3.3.3.2

Move the negative in front of the fraction.

$a = - \frac{7}{3}$

$a = - \frac{7}{3}$

$a = - \frac{7}{3}$

$a = - \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{7}{3}$

Decimal Form:

$a = - 2.\overline{3}$

Mixed Number Form:

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$