Solve for x x/5-1/2=x/6

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

Move $\frac{x}{6}$ to the left side of the equation by subtracting it from both sides.

$\frac{x}{5} - \frac{1}{2} - \frac{x}{6} = 0$

Simplify $\frac{x}{5} - \frac{1}{2} - \frac{x}{6}$ .

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To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{5} \cdot \frac{6}{6} - \frac{x}{6} - \frac{1}{2} = 0$

To write $- \frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} \cdot \frac{6}{6} - \frac{x}{6} \cdot \frac{5}{5} - \frac{1}{2} = 0$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{x}{5}$ and $\frac{6}{6}$ .

$\frac{x \cdot 6}{5 \cdot 6} - \frac{x}{6} \cdot \frac{5}{5} - \frac{1}{2} = 0$

Multiply $5$ by $6$ .

$\frac{x \cdot 6}{30} - \frac{x}{6} \cdot \frac{5}{5} - \frac{1}{2} = 0$

Multiply $\frac{x}{6}$ and $\frac{5}{5}$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{6 \cdot 5} - \frac{1}{2} = 0$

Multiply $6$ by $5$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{30} - \frac{1}{2} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - x \cdot 5}{30} - \frac{1}{2} = 0$

Simplify each term.

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Simplify the numerator.

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Factor $x$ out of $x \cdot 6 - x \cdot 5$ .

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Factor $x$ out of $x \cdot 6$ .

$\frac{x (6) - x \cdot 5}{30} - \frac{1}{2} = 0$

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (6) + x (- 1 \cdot 5)}{30} - \frac{1}{2} = 0$

Factor $x$ out of $x (6) + x (- 1 \cdot 5)$ .

$\frac{x (6 - 1 \cdot 5)}{30} - \frac{1}{2} = 0$

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{30} - \frac{1}{2} = 0$

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{30} - \frac{1}{2} = 0$

Multiply $x$ by $1$ .

$\frac{x}{30} - \frac{1}{2} = 0$

Find the LCD of the terms in the equation.

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To find the LCD of a set of numbers $(\frac{x}{30}, - \frac{1}{2})$ , find the LCM of the denominators.

$LCM (30, 2)$

Calculate the LCM of first two denominators in the list, $30$ and $2$ .

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Find the values of the numerical part of each term. Select the largest one, which in this case is $30$ . Multiply them together to get the current total. In this case, the current total is $60$ .

Current Total = $60$

Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.

$30$

Multiply each term by $30$ and simplify.

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Multiply each term in $\frac{x}{30} - \frac{1}{2} = 0$ by $30$ .

$\frac{x}{30} \cdot 30 - \frac{1}{2} \cdot 30 = 0 \cdot 30$

Simplify each term.

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Cancel the common factor of $30$ .

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Cancel the common factor.

$\frac{x}{30} \cdot 30 - \frac{1}{2} \cdot 30 = 0 \cdot 30$

Rewrite the expression.

$x - \frac{1}{2} \cdot 30 = 0 \cdot 30$

Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x + \frac{- 1}{2} \cdot 30 = 0 \cdot 30$

Factor $2$ out of $30$ .

$x + \frac{- 1}{2} \cdot (2 (15)) = 0 \cdot 30$

Cancel the common factor.

$x + \frac{- 1}{2} \cdot (2 \cdot 15) = 0 \cdot 30$

Rewrite the expression.

$x - 1 \cdot 15 = 0 \cdot 30$

Multiply $- 1$ by $15$ .

$x - 15 = 0 \cdot 30$

Multiply $0$ by $30$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

Solve for x x/5-1/2=x/6

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