Precalculus Examples

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

Step 1

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

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

Step 2

Combine $\frac{1}{4}$ and $x$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $x$ from $7 x$ .

$1 + \frac{6 x}{4} = \frac{1}{4}$

Step 3.4

Cancel the common factor of $6$ and $4$ .

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Step 3.4.1

Factor $2$ out of $6 x$ .

$1 + \frac{2 (3 x)}{4} = \frac{1}{4}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

$1 + \frac{2 (3 x)}{2 (2)} = \frac{1}{4}$

Step 3.4.2.2

Cancel the common factor.

$1 + \frac{2 (3 x)}{2 \cdot 2} = \frac{1}{4}$

Step 3.4.2.3

Rewrite the expression.

$1 + \frac{3 x}{2} = \frac{1}{4}$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$\frac{3 x}{2} = \frac{1}{4} - 1$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{2} = \frac{1}{4} - 1 \cdot \frac{4}{4}$

Step 4.3

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{3 x}{2} = \frac{1}{4} + \frac{- 1 \cdot 4}{4}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{3 x}{2} = \frac{1 - 1 \cdot 4}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $4$ .

$\frac{3 x}{2} = \frac{1 - 4}{4}$

Step 4.5.2

Subtract $4$ from $1$ .

$\frac{3 x}{2} = \frac{- 3}{4}$

Step 4.6

Move the negative in front of the fraction.

$\frac{3 x}{2} = - \frac{3}{4}$

Step 5

Multiply both sides of the equation by $\frac{2}{3}$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} (- \frac{3}{4})$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} (- \frac{3}{4})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} (- \frac{3}{4})$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} (- \frac{3}{4})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{2}{3} (- \frac{3}{4})$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Step 6.2.1.1.2

Factor $2$ out of $4$ .

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

Step 6.2.1.1.3

Cancel the common factor.

$x = \frac{2}{3} \cdot \frac{- 3}{2 \cdot 2}$

Step 6.2.1.1.4

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{- 3}{2}$

Step 6.2.1.2

Cancel the common factor of $3$ .

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Step 6.2.1.2.1

Factor $3$ out of $- 3$ .

$x = \frac{1}{3} \cdot \frac{3 (- 1)}{2}$

Step 6.2.1.2.2

Cancel the common factor.

$x = \frac{1}{3} \cdot \frac{3 \cdot - 1}{2}$

Step 6.2.1.2.3

Rewrite the expression.

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

Step 6.2.1.3

Move the negative in front of the fraction.

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

Step 7