Algebra Examples

$\frac{2 x + 1}{3} - \frac{x - 1}{2} = \frac{5}{6}$

Step 1

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

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Step 1.1

To write $\frac{2 x + 1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x + 1}{3} \cdot \frac{2}{2} - \frac{x - 1}{2} = \frac{5}{6}$

Step 1.2

To write $- \frac{x - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x + 1}{3} \cdot \frac{2}{2} - \frac{x - 1}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2 x + 1}{3}$ by $\frac{2}{2}$ .

$\frac{(2 x + 1) \cdot 2}{3 \cdot 2} - \frac{x - 1}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{(2 x + 1) \cdot 2}{6} - \frac{x - 1}{2} \cdot \frac{3}{3} = \frac{5}{6}$

Step 1.3.3

Multiply $\frac{x - 1}{2}$ by $\frac{3}{3}$ .

$\frac{(2 x + 1) \cdot 2}{6} - \frac{(x - 1) \cdot 3}{2 \cdot 3} = \frac{5}{6}$

Step 1.3.4

Multiply $2$ by $3$ .

$\frac{(2 x + 1) \cdot 2}{6} - \frac{(x - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(2 x + 1) \cdot 2 - (x - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{2 x \cdot 2 + 1 \cdot 2 - (x - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5.2

Multiply $2$ by $2$ .

$\frac{4 x + 1 \cdot 2 - (x - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5.3

Multiply $2$ by $1$ .

$\frac{4 x + 2 - (x - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5.4

Apply the distributive property.

$\frac{4 x + 2 + (- x - - 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5.5

Multiply $- 1$ by $- 1$ .

$\frac{4 x + 2 + (- x + 1) \cdot 3}{6} = \frac{5}{6}$

Step 1.5.6

Apply the distributive property.

$\frac{4 x + 2 - x \cdot 3 + 1 \cdot 3}{6} = \frac{5}{6}$

Step 1.5.7

Multiply $3$ by $- 1$ .

$\frac{4 x + 2 - 3 x + 1 \cdot 3}{6} = \frac{5}{6}$

Step 1.5.8

Multiply $3$ by $1$ .

$\frac{4 x + 2 - 3 x + 3}{6} = \frac{5}{6}$

Step 1.5.9

Subtract $3 x$ from $4 x$ .

$\frac{x + 2 + 3}{6} = \frac{5}{6}$

Step 1.5.10

Add $2$ and $3$ .

$\frac{x + 5}{6} = \frac{5}{6}$

Step 2

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

$x + 5 = 5$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$x = 5 - 5$

Step 3.2

Subtract $5$ from $5$ .

$x = 0$