Algebra Examples

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

Step 1

Since $f$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Simplify $f - \frac{3}{4} f + 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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

Step 2.3

Combine $f$ and $\frac{4}{4}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $3 f$ from $f \cdot 4$ .

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Step 2.5.1

Reorder $f$ and $4$ .

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

Step 2.5.2

Subtract $3 f$ from $4 \cdot f$ .

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

Step 3

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

$\frac{f}{4} + 3 = 2 - \frac{f}{4}$

Step 4

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

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Step 4.1

Add $\frac{f}{4}$ to both sides of the equation.

$\frac{f}{4} + 3 + \frac{f}{4} = 2$

Step 4.2

Combine the numerators over the common denominator.

$3 + \frac{f + f}{4} = 2$

Step 4.3

Add $f$ and $f$ .

$3 + \frac{2 f}{4} = 2$

Step 4.4

Cancel the common factor of $2$ and $4$ .

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Step 4.4.1

Factor $2$ out of $2 f$ .

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

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $4$ .

$3 + \frac{2 f}{2 \cdot 2} = 2$

Step 4.4.2.2

Cancel the common factor.

$3 + \frac{2 f}{2 \cdot 2} = 2$

Step 4.4.2.3

Rewrite the expression.

$3 + \frac{f}{2} = 2$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$\frac{f}{2} = 2 - 3$

Step 5.2

Subtract $3$ from $2$ .

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

Step 6

Multiply both sides of the equation by $2$ .

$2 \frac{f}{2} = 2 \cdot - 1$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Cancel the common factor of $2$ .

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Step 7.1.1.1

Cancel the common factor.

$2 \frac{f}{2} = 2 \cdot - 1$

Step 7.1.1.2

Rewrite the expression.

$f = 2 \cdot - 1$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $2$ by $- 1$ .

$f = - 2$