Algebra Examples

$2 x - \frac{2 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1

Simplify $2 x - \frac{2 x}{7}$ .

Tap for more steps...

Step 1.1

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 x \cdot \frac{7}{7} - \frac{2 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

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

$\frac{2 x \cdot 7}{7} - \frac{2 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2 x \cdot 7 - 2 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.3

Simplify the numerator.

Tap for more steps...

Step 1.3.1

Factor $2 x$ out of $2 x \cdot 7 - 2 x$ .

Tap for more steps...

Step 1.3.1.1

Factor $2 x$ out of $2 x \cdot 7$ .

$\frac{2 x (7) - 2 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.3.1.2

Factor $2 x$ out of $- 2 x$ .

$\frac{2 x (7) + 2 x (- 1)}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.3.1.3

Factor $2 x$ out of $2 x (7) + 2 x (- 1)$ .

$\frac{2 x (7 - 1)}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.3.2

Subtract $1$ from $7$ .

$\frac{2 x \cdot 6}{7} = \frac{x}{2} + \frac{17}{2}$

Step 1.3.3

Multiply $6$ by $2$ .

$\frac{12 x}{7} = \frac{x}{2} + \frac{17}{2}$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{12 x}{7} - \frac{x}{2} = \frac{17}{2}$

Step 2.2

To write $\frac{12 x}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12 x}{7} \cdot \frac{2}{2} - \frac{x}{2} = \frac{17}{2}$

Step 2.3

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{12 x}{7} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{7}{7} = \frac{17}{2}$

Step 2.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

Multiply $\frac{12 x}{7}$ by $\frac{2}{2}$ .

$\frac{12 x \cdot 2}{7 \cdot 2} - \frac{x}{2} \cdot \frac{7}{7} = \frac{17}{2}$

Step 2.4.2

Multiply $7$ by $2$ .

$\frac{12 x \cdot 2}{14} - \frac{x}{2} \cdot \frac{7}{7} = \frac{17}{2}$

Step 2.4.3

Multiply $\frac{x}{2}$ by $\frac{7}{7}$ .

$\frac{12 x \cdot 2}{14} - \frac{x \cdot 7}{2 \cdot 7} = \frac{17}{2}$

Step 2.4.4

Multiply $2$ by $7$ .

$\frac{12 x \cdot 2}{14} - \frac{x \cdot 7}{14} = \frac{17}{2}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{12 x \cdot 2 - x \cdot 7}{14} = \frac{17}{2}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Factor $x$ out of $12 x \cdot 2 - x \cdot 7$ .

Tap for more steps...

Step 2.6.1.1

Factor $x$ out of $12 x \cdot 2$ .

$\frac{x (12 \cdot 2) - x \cdot 7}{14} = \frac{17}{2}$

Step 2.6.1.2

Factor $x$ out of $- x \cdot 7$ .

$\frac{x (12 \cdot 2) + x (- 1 \cdot 7)}{14} = \frac{17}{2}$

Step 2.6.1.3

Factor $x$ out of $x (12 \cdot 2) + x (- 1 \cdot 7)$ .

$\frac{x (12 \cdot 2 - 1 \cdot 7)}{14} = \frac{17}{2}$

Step 2.6.2

Multiply $12$ by $2$ .

$\frac{x (24 - 1 \cdot 7)}{14} = \frac{17}{2}$

Step 2.6.3

Multiply $- 1$ by $7$ .

$\frac{x (24 - 7)}{14} = \frac{17}{2}$

Step 2.6.4

Subtract $7$ from $24$ .

$\frac{x \cdot 17}{14} = \frac{17}{2}$

Step 2.7

Move $17$ to the left of $x$ .

$\frac{17 x}{14} = \frac{17}{2}$

Step 3

Multiply both sides of the equation by $\frac{14}{17}$ .

$\frac{14}{17} \cdot \frac{17 x}{14} = \frac{14}{17} \cdot \frac{17}{2}$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $\frac{14}{17} \cdot \frac{17 x}{14}$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $14$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{14}{17} \cdot \frac{17 x}{14} = \frac{14}{17} \cdot \frac{17}{2}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{17} (17 x) = \frac{14}{17} \cdot \frac{17}{2}$

Step 4.1.1.2

Cancel the common factor of $17$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $17$ out of $17 x$ .

$\frac{1}{17} (17 (x)) = \frac{14}{17} \cdot \frac{17}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{17} (17 x) = \frac{14}{17} \cdot \frac{17}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{14}{17} \cdot \frac{17}{2}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{14}{17} \cdot \frac{17}{2}$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.1

Factor $2$ out of $14$ .

$x = \frac{2 (7)}{17} \cdot \frac{17}{2}$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{2 \cdot 7}{17} \cdot \frac{17}{2}$

Step 4.2.1.1.3

Rewrite the expression.

$x = \frac{7}{17} \cdot 17$

Step 4.2.1.2

Cancel the common factor of $17$ .

Tap for more steps...

Step 4.2.1.2.1

Cancel the common factor.

$x = \frac{7}{17} \cdot 17$

Step 4.2.1.2.2

Rewrite the expression.

$x = 7$