Basic Math Examples

$(x - \frac{1}{7}) + \frac{x - \frac{1}{7}}{2} = 234$

Step 1

Simplify $x - \frac{1}{7} + \frac{x - \frac{1}{7}}{2}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Simplify the numerator.

Tap for more steps...

Step 1.1.1.1

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

$x - \frac{1}{7} + \frac{x \cdot \frac{7}{7} - \frac{1}{7}}{2} = 234$

Step 1.1.1.2

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

$x - \frac{1}{7} + \frac{\frac{x \cdot 7}{7} - \frac{1}{7}}{2} = 234$

Step 1.1.1.3

Combine the numerators over the common denominator.

$x - \frac{1}{7} + \frac{\frac{x \cdot 7 - 1}{7}}{2} = 234$

Step 1.1.1.4

Move $7$ to the left of $x$ .

$x - \frac{1}{7} + \frac{\frac{7 x - 1}{7}}{2} = 234$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$x - \frac{1}{7} + \frac{7 x - 1}{7} \cdot \frac{1}{2} = 234$

Step 1.1.3

Multiply $\frac{7 x - 1}{7} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 1.1.3.1

Multiply $\frac{7 x - 1}{7}$ by $\frac{1}{2}$ .

$x - \frac{1}{7} + \frac{7 x - 1}{7 \cdot 2} = 234$

Step 1.1.3.2

Multiply $7$ by $2$ .

$x - \frac{1}{7} + \frac{7 x - 1}{14} = 234$

Step 1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$x \cdot \frac{14}{14} + \frac{7 x - 1}{14} - \frac{1}{7} = 234$

Step 1.3

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

$\frac{x \cdot 14}{14} + \frac{7 x - 1}{14} - \frac{1}{7} = 234$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 14 + 7 x - 1}{14} - \frac{1}{7} = 234$

Step 1.5

Add $x \cdot 14$ and $7 x$ .

Tap for more steps...

Step 1.5.1

Reorder $x$ and $14$ .

$\frac{14 \cdot x + 7 x - 1}{14} - \frac{1}{7} = 234$

Step 1.5.2

Add $14 \cdot x$ and $7 x$ .

$\frac{21 \cdot x - 1}{14} - \frac{1}{7} = 234$

Step 1.6

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{21 x - 1}{14} - \frac{1}{7} \cdot \frac{2}{2} = 234$

Step 1.7

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

Tap for more steps...

Step 1.7.1

Multiply $\frac{1}{7}$ by $\frac{2}{2}$ .

$\frac{21 x - 1}{14} - \frac{2}{7 \cdot 2} = 234$

Step 1.7.2

Multiply $7$ by $2$ .

$\frac{21 x - 1}{14} - \frac{2}{14} = 234$

Step 1.8

Combine the numerators over the common denominator.

$\frac{21 x - 1 - 2}{14} = 234$

Step 1.9

Simplify the numerator.

Tap for more steps...

Step 1.9.1

Subtract $2$ from $- 1$ .

$\frac{21 x - 3}{14} = 234$

Step 1.9.2

Factor $3$ out of $21 x - 3$ .

Tap for more steps...

Step 1.9.2.1

Factor $3$ out of $21 x$ .

$\frac{3 (7 x) - 3}{14} = 234$

Step 1.9.2.2

Factor $3$ out of $- 3$ .

$\frac{3 (7 x) + 3 (- 1)}{14} = 234$

Step 1.9.2.3

Factor $3$ out of $3 (7 x) + 3 (- 1)$ .

$\frac{3 (7 x - 1)}{14} = 234$

Step 2

Multiply both sides by $14$ .

$\frac{3 (7 x - 1)}{14} \cdot 14 = 234 \cdot 14$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{3 (7 x - 1)}{14} \cdot 14$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $14$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{3 (7 x - 1)}{14} \cdot 14 = 234 \cdot 14$

Step 3.1.1.1.2

Rewrite the expression.

$3 (7 x - 1) = 234 \cdot 14$

Step 3.1.1.2

Apply the distributive property.

$3 (7 x) + 3 \cdot - 1 = 234 \cdot 14$

Step 3.1.1.3

Multiply.

Tap for more steps...

Step 3.1.1.3.1

Multiply $7$ by $3$ .

$21 x + 3 \cdot - 1 = 234 \cdot 14$

Step 3.1.1.3.2

Multiply $3$ by $- 1$ .

$21 x - 3 = 234 \cdot 14$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $234$ by $14$ .

$21 x - 3 = 3276$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $3$ to both sides of the equation.

$21 x = 3276 + 3$

Step 4.1.2

Add $3276$ and $3$ .

$21 x = 3279$

Step 4.2

Divide each term in $21 x = 3279$ by $21$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $21 x = 3279$ by $21$ .

$\frac{21 x}{21} = \frac{3279}{21}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $21$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{21 x}{21} = \frac{3279}{21}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3279}{21}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Cancel the common factor of $3279$ and $21$ .

Tap for more steps...

Step 4.2.3.1.1

Factor $3$ out of $3279$ .

$x = \frac{3 (1093)}{21}$

Step 4.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.2.3.1.2.1

Factor $3$ out of $21$ .

$x = \frac{3 \cdot 1093}{3 \cdot 7}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 1093}{3 \cdot 7}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{1093}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1093}{7}$

Decimal Form:

$x = 156.14285714 \dots$

Mixed Number Form:

$x = 156 \frac{1}{7}$