Algebra Examples

$3 \frac{1}{3} (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Simplify $3 \frac{1}{3} (1 + 2 x)$ .

Tap for more steps...

Step 1.1.1

Convert $3 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(3 + \frac{1}{3}) (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.1.2

Add $3$ and $\frac{1}{3}$ .

Tap for more steps...

Step 1.1.1.2.1

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

$(3 \cdot \frac{3}{3} + \frac{1}{3}) (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.1.2.2

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

$(\frac{3 \cdot 3}{3} + \frac{1}{3}) (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 1}{3} (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.1.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.1.2.4.2

Add $9$ and $1$ .

$\frac{10}{3} (1 + 2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.2

Apply the distributive property.

$\frac{10}{3} \cdot 1 + \frac{10}{3} (2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.3

Multiply $\frac{10}{3}$ by $1$ .

$\frac{10}{3} + \frac{10}{3} (2 x) = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.4

Multiply $\frac{10}{3} (2 x)$ .

Tap for more steps...

Step 1.1.4.1

Combine $2$ and $\frac{10}{3}$ .

$\frac{10}{3} + \frac{2 \cdot 10}{3} x = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.4.2

Multiply $2$ by $10$ .

$\frac{10}{3} + \frac{20}{3} x = 5 \frac{1}{2} (2 x - 1)$

Step 1.1.4.3

Combine $\frac{20}{3}$ and $x$ .

$\frac{10}{3} + \frac{20 x}{3} = 5 \frac{1}{2} (2 x - 1)$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Simplify $5 \frac{1}{2} (2 x - 1)$ .

Tap for more steps...

Step 2.1.1

Convert $5 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{10}{3} + \frac{20 x}{3} = (5 + \frac{1}{2}) (2 x - 1)$

Step 2.1.1.2

Add $5$ and $\frac{1}{2}$ .

Tap for more steps...

Step 2.1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{10}{3} + \frac{20 x}{3} = (5 \cdot \frac{2}{2} + \frac{1}{2}) (2 x - 1)$

Step 2.1.1.2.2

Combine $5$ and $\frac{2}{2}$ .

$\frac{10}{3} + \frac{20 x}{3} = (\frac{5 \cdot 2}{2} + \frac{1}{2}) (2 x - 1)$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{10}{3} + \frac{20 x}{3} = \frac{5 \cdot 2 + 1}{2} (2 x - 1)$

Step 2.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.1.2.4.1

Multiply $5$ by $2$ .

$\frac{10}{3} + \frac{20 x}{3} = \frac{10 + 1}{2} (2 x - 1)$

Step 2.1.1.2.4.2

Add $10$ and $1$ .

$\frac{10}{3} + \frac{20 x}{3} = \frac{11}{2} (2 x - 1)$

Step 2.1.2

Apply the distributive property.

$\frac{10}{3} + \frac{20 x}{3} = \frac{11}{2} (2 x) + \frac{11}{2} \cdot - 1$

Step 2.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.3.1

Factor $2$ out of $2 x$ .

$\frac{10}{3} + \frac{20 x}{3} = \frac{11}{2} (2 (x)) + \frac{11}{2} \cdot - 1$

Step 2.1.3.2

Cancel the common factor.

$\frac{10}{3} + \frac{20 x}{3} = \frac{11}{2} (2 x) + \frac{11}{2} \cdot - 1$

Step 2.1.3.3

Rewrite the expression.

$\frac{10}{3} + \frac{20 x}{3} = 11 x + \frac{11}{2} \cdot - 1$

Step 2.1.4

Multiply $\frac{11}{2} \cdot - 1$ .

Tap for more steps...

Step 2.1.4.1

Combine $\frac{11}{2}$ and $- 1$ .

$\frac{10}{3} + \frac{20 x}{3} = 11 x + \frac{11 \cdot - 1}{2}$

Step 2.1.4.2

Multiply $11$ by $- 1$ .

$\frac{10}{3} + \frac{20 x}{3} = 11 x + \frac{- 11}{2}$

Step 2.1.5

Move the negative in front of the fraction.

$\frac{10}{3} + \frac{20 x}{3} = 11 x - \frac{11}{2}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $11 x$ from both sides of the equation.

$\frac{10}{3} + \frac{20 x}{3} - 11 x = - \frac{11}{2}$

Step 3.2

To write $- 11 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10}{3} + \frac{20 x}{3} - 11 x \cdot \frac{3}{3} = - \frac{11}{2}$

Step 3.3

Combine $- 11 x$ and $\frac{3}{3}$ .

$\frac{10}{3} + \frac{20 x}{3} + \frac{- 11 x \cdot 3}{3} = - \frac{11}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{10}{3} + \frac{20 x - 11 x \cdot 3}{3} = - \frac{11}{2}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{10 + 20 x - 11 x \cdot 3}{3} = - \frac{11}{2}$

Step 3.6

Multiply $3$ by $- 11$ .

$\frac{10 + 20 x - 33 x}{3} = - \frac{11}{2}$

Step 3.7

Subtract $33 x$ from $20 x$ .

$\frac{10 - 13 x}{3} = - \frac{11}{2}$

Step 4

Multiply both sides by $3$ .

$\frac{10 - 13 x}{3} \cdot 3 = - \frac{11}{2} \cdot 3$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $\frac{10 - 13 x}{3} \cdot 3$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1.1.1.1

Cancel the common factor.

$\frac{10 - 13 x}{3} \cdot 3 = - \frac{11}{2} \cdot 3$

Step 5.1.1.1.2

Rewrite the expression.

$10 - 13 x = - \frac{11}{2} \cdot 3$

Step 5.1.1.2

Reorder $10$ and $- 13 x$ .

$- 13 x + 10 = - \frac{11}{2} \cdot 3$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $- \frac{11}{2} \cdot 3$ .

Tap for more steps...

Step 5.2.1.1

Multiply $- \frac{11}{2} \cdot 3$ .

Tap for more steps...

Step 5.2.1.1.1

Multiply $3$ by $- 1$ .

$- 13 x + 10 = - 3 (\frac{11}{2})$

Step 5.2.1.1.2

Combine $- 3$ and $\frac{11}{2}$ .

$- 13 x + 10 = \frac{- 3 \cdot 11}{2}$

Step 5.2.1.1.3

Multiply $- 3$ by $11$ .

$- 13 x + 10 = \frac{- 33}{2}$

Step 5.2.1.2

Move the negative in front of the fraction.

$- 13 x + 10 = - \frac{33}{2}$

Step 6

Solve for $x$ .

Tap for more steps...

Step 6.1

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

Tap for more steps...

Step 6.1.1

Subtract $10$ from both sides of the equation.

$- 13 x = - \frac{33}{2} - 10$

Step 6.1.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 13 x = - \frac{33}{2} - 10 \cdot \frac{2}{2}$

Step 6.1.3

Combine $- 10$ and $\frac{2}{2}$ .

$- 13 x = - \frac{33}{2} + \frac{- 10 \cdot 2}{2}$

Step 6.1.4

Combine the numerators over the common denominator.

$- 13 x = \frac{- 33 - 10 \cdot 2}{2}$

Step 6.1.5

Simplify the numerator.

Tap for more steps...

Step 6.1.5.1

Multiply $- 10$ by $2$ .

$- 13 x = \frac{- 33 - 20}{2}$

Step 6.1.5.2

Subtract $20$ from $- 33$ .

$- 13 x = \frac{- 53}{2}$

Step 6.1.6

Move the negative in front of the fraction.

$- 13 x = - \frac{53}{2}$

Step 6.2

Divide each term in $- 13 x = - \frac{53}{2}$ by $- 13$ and simplify.

Tap for more steps...

Step 6.2.1

Divide each term in $- 13 x = - \frac{53}{2}$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- \frac{53}{2}}{- 13}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $- 13$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- \frac{53}{2}}{- 13}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{53}{2}}{- 13}$

Step 6.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{53}{2} \cdot \frac{1}{- 13}$

Step 6.2.3.2

Move the negative in front of the fraction.

$x = - \frac{53}{2} (- \frac{1}{13})$

Step 6.2.3.3

Multiply $- \frac{53}{2} (- \frac{1}{13})$ .

Tap for more steps...

Step 6.2.3.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{53}{2}) \frac{1}{13}$

Step 6.2.3.3.2

Multiply $\frac{53}{2}$ by $1$ .

$x = \frac{53}{2} \cdot \frac{1}{13}$

Step 6.2.3.3.3

Multiply $\frac{53}{2}$ by $\frac{1}{13}$ .

$x = \frac{53}{2 \cdot 13}$

Step 6.2.3.3.4

Multiply $2$ by $13$ .

$x = \frac{53}{26}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{53}{26}$

Decimal Form:

$x = 2.03846153 \dots$

Mixed Number Form:

$x = 2 \frac{1}{26}$