Algebra Examples

$\frac{3}{4} x - \frac{x - 14}{6} = \frac{7}{4} x$

Step 1

Simplify $\frac{3}{4} x - \frac{x - 14}{6}$ .

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Step 1.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} - \frac{x - 14}{6} = \frac{7}{4} x$

Step 1.2

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{x - 14}{6} = \frac{7}{4} x$

Step 1.3

To write $- \frac{x - 14}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{x - 14}{6} \cdot \frac{2}{2} = \frac{7}{4} x$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{4 \cdot 3} - \frac{x - 14}{6} \cdot \frac{2}{2} = \frac{7}{4} x$

Step 1.4.2

Multiply $4$ by $3$ .

$\frac{3 x \cdot 3}{12} - \frac{x - 14}{6} \cdot \frac{2}{2} = \frac{7}{4} x$

Step 1.4.3

Multiply $\frac{x - 14}{6}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 3}{12} - \frac{(x - 14) \cdot 2}{6 \cdot 2} = \frac{7}{4} x$

Step 1.4.4

Multiply $6$ by $2$ .

$\frac{3 x \cdot 3}{12} - \frac{(x - 14) \cdot 2}{12} = \frac{7}{4} x$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - (x - 14) \cdot 2}{12} = \frac{7}{4} x$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $3$ .

$\frac{9 x - (x - 14) \cdot 2}{12} = \frac{7}{4} x$

Step 1.6.2

Apply the distributive property.

$\frac{9 x + (- x - - 14) \cdot 2}{12} = \frac{7}{4} x$

Step 1.6.3

Multiply $- 1$ by $- 14$ .

$\frac{9 x + (- x + 14) \cdot 2}{12} = \frac{7}{4} x$

Step 1.6.4

Apply the distributive property.

$\frac{9 x - x \cdot 2 + 14 \cdot 2}{12} = \frac{7}{4} x$

Step 1.6.5

Multiply $2$ by $- 1$ .

$\frac{9 x - 2 x + 14 \cdot 2}{12} = \frac{7}{4} x$

Step 1.6.6

Multiply $14$ by $2$ .

$\frac{9 x - 2 x + 28}{12} = \frac{7}{4} x$

Step 1.6.7

Subtract $2 x$ from $9 x$ .

$\frac{7 x + 28}{12} = \frac{7}{4} x$

Step 1.6.8

Factor $7$ out of $7 x + 28$ .

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Step 1.6.8.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) + 28}{12} = \frac{7}{4} x$

Step 1.6.8.2

Factor $7$ out of $28$ .

$\frac{7 x + 7 \cdot 4}{12} = \frac{7}{4} x$

Step 1.6.8.3

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

$\frac{7 (x + 4)}{12} = \frac{7}{4} x$

Step 2

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

$\frac{7 (x + 4)}{12} = \frac{7 x}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{7 x}{4}$ from both sides of the equation.

$\frac{7 (x + 4)}{12} - \frac{7 x}{4} = 0$

Step 3.2

To write $- \frac{7 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7 (x + 4)}{12} - \frac{7 x}{4} \cdot \frac{3}{3} = 0$

Step 3.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{7 x}{4}$ by $\frac{3}{3}$ .

$\frac{7 (x + 4)}{12} - \frac{7 x \cdot 3}{4 \cdot 3} = 0$

Step 3.3.2

Multiply $4$ by $3$ .

$\frac{7 (x + 4)}{12} - \frac{7 x \cdot 3}{12} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{7 (x + 4) - 7 x \cdot 3}{12} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $7$ out of $7 (x + 4) - 7 x \cdot 3$ .

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Step 3.5.1.1

Factor $7$ out of $- 7 x \cdot 3$ .

$\frac{7 (x + 4) + 7 (- x \cdot 3)}{12} = 0$

Step 3.5.1.2

Factor $7$ out of $7 (x + 4) + 7 (- x \cdot 3)$ .

$\frac{7 (x + 4 - x \cdot 3)}{12} = 0$

Step 3.5.2

Multiply $3$ by $- 1$ .

$\frac{7 (x + 4 - 3 x)}{12} = 0$

Step 3.5.3

Subtract $3 x$ from $x$ .

$\frac{7 (- 2 x + 4)}{12} = 0$

Step 3.5.4

Factor $2$ out of $- 2 x + 4$ .

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Step 3.5.4.1

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

$\frac{7 (2 (- x) + 4)}{12} = 0$

Step 3.5.4.2

Factor $2$ out of $4$ .

$\frac{7 (2 (- x) + 2 (2))}{12} = 0$

Step 3.5.4.3

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

$\frac{7 (2 (- x + 2))}{12} = 0$

$\frac{7 \cdot 2 (- x + 2)}{12} = 0$

Step 3.5.5

Multiply $7$ by $2$ .

$\frac{14 (- x + 2)}{12} = 0$

Step 3.6

Cancel the common factor of $14$ and $12$ .

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Step 3.6.1

Factor $2$ out of $14 (- x + 2)$ .

$\frac{2 (7 (- x + 2))}{12} = 0$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $2$ out of $12$ .

$\frac{2 (7 (- x + 2))}{2 (6)} = 0$

Step 3.6.2.2

Cancel the common factor.

$\frac{2 (7 (- x + 2))}{2 \cdot 6} = 0$

Step 3.6.2.3

Rewrite the expression.

$\frac{7 (- x + 2)}{6} = 0$

Step 3.7

Factor $- 1$ out of $- x$ .

$\frac{7 (- (x) + 2)}{6} = 0$

Step 3.8

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{7 (- (x) - 1 (- 2))}{6} = 0$

Step 3.9

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

$\frac{7 (- (x - 2))}{6} = 0$

Step 3.10

Rewrite $- (x - 2)$ as $- 1 (x - 2)$ .

$\frac{7 (- 1 (x - 2))}{6} = 0$

Step 3.11

Move the negative in front of the fraction.

$- \frac{7 (x - 2)}{6} = 0$

Step 4

Set the numerator equal to zero.

$7 (x - 2) = 0$

Step 5

Solve the equation for $x$ .

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Step 5.1

Divide each term in $7 (x - 2) = 0$ by $7$ and simplify.

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Step 5.1.1

Divide each term in $7 (x - 2) = 0$ by $7$ .

$\frac{7 (x - 2)}{7} = \frac{0}{7}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $7$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{7 (x - 2)}{7} = \frac{0}{7}$

Step 5.1.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{0}{7}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $0$ by $7$ .

$x - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$x = 2$