Basic Math Examples

$2 a + 3 = \frac{1}{2} \cdot (6 + a)$

Step 1

Simplify $\frac{1}{2} \cdot (6 + a)$ .

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Step 1.1

Rewrite.

$2 a + 3 = 0 + 0 + \frac{1}{2} \cdot (6 + a)$

Step 1.2

Simplify by adding zeros.

$2 a + 3 = \frac{1}{2} \cdot (6 + a)$

Step 1.3

Apply the distributive property.

$2 a + 3 = \frac{1}{2} \cdot 6 + \frac{1}{2} a$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $6$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

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

$2 a + 3 = 3 + \frac{a}{2}$

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

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 $a$ out of $2 a \cdot 2 - a$ .

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Step 2.5.1.1.1

Factor $a$ out of $2 a \cdot 2$ .

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

Step 2.5.1.1.2

Factor $a$ out of $- a$ .

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

Step 2.5.1.1.3

Factor $a$ out of $a (2 \cdot 2) + a \cdot - 1$ .

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

Step 2.5.1.2

Multiply $2$ by $2$ .

$\frac{a (4 - 1)}{2} + 3 = 3$

Step 2.5.1.3

Subtract $1$ from $4$ .

$\frac{a \cdot 3}{2} + 3 = 3$

Step 2.5.2

Move $3$ to the left of $a$ .

$\frac{3 a}{2} + 3 = 3$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

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

Step 3.2

Subtract $3$ from $3$ .

$\frac{3 a}{2} = 0$

Step 4

Set the numerator equal to zero.

$3 a = 0$

Step 5

Divide each term in $3 a = 0$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 a = 0$ by $3$ .

$\frac{3 a}{3} = \frac{0}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 a}{3} = \frac{0}{3}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{0}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $3$ .

$a = 0$