Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1.1

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

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

Step 1.1.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

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

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

Step 1.1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 1}{3} (2 x - 3) = 2 \frac{1}{3}$

Step 1.1.1.2.4.2

Add $6$ and $1$ .

$\frac{7}{3} (2 x - 3) = 2 \frac{1}{3}$

Step 1.1.2

Apply the distributive property.

$\frac{7}{3} (2 x) + \frac{7}{3} \cdot - 3 = 2 \frac{1}{3}$

Step 1.1.3

Multiply $\frac{7}{3} (2 x)$ .

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Step 1.1.3.1

Combine $2$ and $\frac{7}{3}$ .

$\frac{2 \cdot 7}{3} x + \frac{7}{3} \cdot - 3 = 2 \frac{1}{3}$

Step 1.1.3.2

Multiply $2$ by $7$ .

$\frac{14}{3} x + \frac{7}{3} \cdot - 3 = 2 \frac{1}{3}$

Step 1.1.3.3

Combine $\frac{14}{3}$ and $x$ .

$\frac{14 x}{3} + \frac{7}{3} \cdot - 3 = 2 \frac{1}{3}$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Factor $3$ out of $- 3$ .

$\frac{14 x}{3} + \frac{7}{3} \cdot (3 (- 1)) = 2 \frac{1}{3}$

Step 1.1.4.2

Cancel the common factor.

$\frac{14 x}{3} + \frac{7}{3} \cdot (3 \cdot - 1) = 2 \frac{1}{3}$

Step 1.1.4.3

Rewrite the expression.

$\frac{14 x}{3} + 7 \cdot - 1 = 2 \frac{1}{3}$

Step 1.1.5

Multiply $7$ by $- 1$ .

$\frac{14 x}{3} - 7 = 2 \frac{1}{3}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1

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

$\frac{14 x}{3} - 7 = 2 + \frac{1}{3}$

Step 2.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 2.1.2.1

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

$\frac{14 x}{3} - 7 = 2 \cdot \frac{3}{3} + \frac{1}{3}$

Step 2.1.2.2

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

$\frac{14 x}{3} - 7 = \frac{2 \cdot 3}{3} + \frac{1}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{14 x}{3} - 7 = \frac{2 \cdot 3 + 1}{3}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $3$ .

$\frac{14 x}{3} - 7 = \frac{6 + 1}{3}$

Step 2.1.2.4.2

Add $6$ and $1$ .

$\frac{14 x}{3} - 7 = \frac{7}{3}$

Step 3

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

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Step 3.1

Add $7$ to both sides of the equation.

$\frac{14 x}{3} = \frac{7}{3} + 7$

Step 3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{14 x}{3} = \frac{7}{3} + 7 \cdot \frac{3}{3}$

Step 3.3

Combine $7$ and $\frac{3}{3}$ .

$\frac{14 x}{3} = \frac{7}{3} + \frac{7 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{14 x}{3} = \frac{7 + 7 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $7$ by $3$ .

$\frac{14 x}{3} = \frac{7 + 21}{3}$

Step 3.5.2

Add $7$ and $21$ .

$\frac{14 x}{3} = \frac{28}{3}$

Step 4

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

$14 x = 28$

Step 5

Divide each term in $14 x = 28$ by $14$ and simplify.

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Step 5.1

Divide each term in $14 x = 28$ by $14$ .

$\frac{14 x}{14} = \frac{28}{14}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $14$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{14 x}{14} = \frac{28}{14}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{14}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $28$ by $14$ .

$x = 2$