Solve for x x/4-1=x/7+5

$\frac{x}{4} - 1 = \frac{x}{7} + 5$

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

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Subtract $\frac{x}{7}$ from both sides of the equation.

$\frac{x}{4} - 1 - \frac{x}{7} = 5$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{4} \cdot \frac{7}{7} - \frac{x}{7} - 1 = 5$

To write $- \frac{x}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{7}{7} - \frac{x}{7} \cdot \frac{4}{4} - 1 = 5$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{x}{4}$ and $\frac{7}{7}$ .

$\frac{x \cdot 7}{4 \cdot 7} - \frac{x}{7} \cdot \frac{4}{4} - 1 = 5$

Multiply $4$ by $7$ .

$\frac{x \cdot 7}{28} - \frac{x}{7} \cdot \frac{4}{4} - 1 = 5$

Multiply $\frac{x}{7}$ and $\frac{4}{4}$ .

$\frac{x \cdot 7}{28} - \frac{x \cdot 4}{7 \cdot 4} - 1 = 5$

Multiply $7$ by $4$ .

$\frac{x \cdot 7}{28} - \frac{x \cdot 4}{28} - 1 = 5$

Combine the numerators over the common denominator.

$\frac{x \cdot 7 - x \cdot 4}{28} - 1 = 5$

Simplify each term.

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Simplify the numerator.

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Factor $x$ out of $x \cdot 7 - x \cdot 4$ .

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

$\frac{x (7) - x \cdot 4}{28} - 1 = 5$

Factor $x$ out of $- x \cdot 4$ .

$\frac{x (7) + x (- 1 \cdot 4)}{28} - 1 = 5$

Factor $x$ out of $x (7) + x (- 1 \cdot 4)$ .

$\frac{x (7 - 1 \cdot 4)}{28} - 1 = 5$

Multiply $- 1$ by $4$ .

$\frac{x (7 - 4)}{28} - 1 = 5$

Subtract $4$ from $7$ .

$\frac{x \cdot 3}{28} - 1 = 5$

Move $3$ to the left of $x$ .

$\frac{3 x}{28} - 1 = 5$

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

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Add $1$ to both sides of the equation.

$\frac{3 x}{28} = 5 + 1$

Add $5$ and $1$ .

$\frac{3 x}{28} = 6$

Multiply both sides of the equation by $\frac{28}{3}$ .

$\frac{28}{3} \cdot \frac{3 x}{28} = \frac{28}{3} \cdot 6$

Simplify both sides of the equation.

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Simplify $\frac{28}{3} \cdot \frac{3 x}{28}$ .

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Cancel the common factor of $28$ .

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Cancel the common factor.

$\frac{28}{3} \cdot \frac{3 x}{28} = \frac{28}{3} \cdot 6$

Rewrite the expression.

$\frac{1}{3} \cdot (3 x) = \frac{28}{3} \cdot 6$

Cancel the common factor of $3$ .

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Factor $3$ out of $3 x$ .

$\frac{1}{3} \cdot (3 (x)) = \frac{28}{3} \cdot 6$

Cancel the common factor.

$\frac{1}{3} \cdot (3 x) = \frac{28}{3} \cdot 6$

Rewrite the expression.

$x = \frac{28}{3} \cdot 6$

Simplify $\frac{28}{3} \cdot 6$ .

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Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$x = \frac{28}{3} \cdot (3 (2))$

Cancel the common factor.

$x = \frac{28}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$x = 28 \cdot 2$

Multiply $28$ by $2$ .

$x = 56$

Solve for x x/4-1=x/7+5

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