Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (q + 1) = \frac{4}{3} - q$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Multiply $\frac{1}{2}$ by $1$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Add $q$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Move $2$ to the left of $q$ .

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

Step 2.7

Add $q$ and $2 q$ .

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

Step 3

Multiply both sides by $2$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $\frac{4}{3} \cdot 2$ .

Tap for more steps...

Step 4.2.1.1

Combine $\frac{4}{3}$ and $2$ .

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

Step 4.2.1.2

Multiply $4$ by $2$ .

$3 q + 1 = \frac{8}{3}$

Step 5

Solve for $q$ .

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Subtract $1$ from both sides of the equation.

$3 q = \frac{8}{3} - 1$

Step 5.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3 q = \frac{8}{3} - 1 \cdot \frac{3}{3}$

Step 5.1.3

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

$3 q = \frac{8}{3} + \frac{- 1 \cdot 3}{3}$

Step 5.1.4

Combine the numerators over the common denominator.

$3 q = \frac{8 - 1 \cdot 3}{3}$

Step 5.1.5

Simplify the numerator.

Tap for more steps...

Step 5.1.5.1

Multiply $- 1$ by $3$ .

$3 q = \frac{8 - 3}{3}$

Step 5.1.5.2

Subtract $3$ from $8$ .

$3 q = \frac{5}{3}$

Step 5.2

Divide each term in $3 q = \frac{5}{3}$ by $3$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $3 q = \frac{5}{3}$ by $3$ .

$\frac{3 q}{3} = \frac{\frac{5}{3}}{3}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{3 q}{3} = \frac{\frac{5}{3}}{3}$

Step 5.2.2.1.2

Divide $q$ by $1$ .

$q = \frac{\frac{5}{3}}{3}$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$q = \frac{5}{3} \cdot \frac{1}{3}$

Step 5.2.3.2

Multiply $\frac{5}{3} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 5.2.3.2.1

Multiply $\frac{5}{3}$ by $\frac{1}{3}$ .

$q = \frac{5}{3 \cdot 3}$

Step 5.2.3.2.2

Multiply $3$ by $3$ .

$q = \frac{5}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$q = \frac{5}{9}$

Decimal Form:

$q = 0.\overline{5}$