Pre-Algebra Examples

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

Step 1

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

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

Step 2

Simplify $\frac{1}{3} \cdot (4 a + 1)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $\frac{1}{3} (4 a)$ .

Tap for more steps...

Step 2.2.1

Combine $4$ and $\frac{1}{3}$ .

$\frac{2 a}{3} + 2 = \frac{4}{3} a + \frac{1}{3} \cdot 1$

Step 2.2.2

Combine $\frac{4}{3}$ and $a$ .

$\frac{2 a}{3} + 2 = \frac{4 a}{3} + \frac{1}{3} \cdot 1$

Step 2.3

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

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

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{4 a}{3}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $4 a$ from $2 a$ .

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

Step 3.4

Move the negative in front of the fraction.

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

Step 4

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

Tap for more steps...

Step 4.1

Subtract $2$ from both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $- 2$ by $3$ .

$- \frac{2 a}{3} = \frac{1 - 6}{3}$

Step 4.5.2

Subtract $6$ from $1$ .

$- \frac{2 a}{3} = \frac{- 5}{3}$

Step 4.6

Move the negative in front of the fraction.

$- \frac{2 a}{3} = - \frac{5}{3}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 2 a = - 5$

Step 6

Divide each term in $- 2 a = - 5$ by $- 2$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $- 2 a = - 5$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 5}{- 2}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 5}{- 2}$

Step 6.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 5}{- 2}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Dividing two negative values results in a positive value.

$a = \frac{5}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5}{2}$

Decimal Form:

$a = 2.5$

Mixed Number Form:

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