Algebra Examples

$\frac{1}{3} (6 f + 5) + \frac{2}{3} (3 f - 1) = \frac{4}{3} f$

Step 1

Simplify $\frac{1}{3} \cdot (6 f + 5) + \frac{2}{3} \cdot (3 f - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{3} (6 f) + \frac{1}{3} \cdot 5 + \frac{2}{3} \cdot (3 f - 1) = \frac{4}{3} f$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Factor $3$ out of $6 f$ .

$\frac{1}{3} (3 (2 f)) + \frac{1}{3} \cdot 5 + \frac{2}{3} \cdot (3 f - 1) = \frac{4}{3} f$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 (2 f)) + \frac{1}{3} \cdot 5 + \frac{2}{3} \cdot (3 f - 1) = \frac{4}{3} f$

Step 1.1.2.3

Rewrite the expression.

$2 f + \frac{1}{3} \cdot 5 + \frac{2}{3} \cdot (3 f - 1) = \frac{4}{3} f$

Step 1.1.3

Combine $\frac{1}{3}$ and $5$ .

$2 f + \frac{5}{3} + \frac{2}{3} \cdot (3 f - 1) = \frac{4}{3} f$

Step 1.1.4

Apply the distributive property.

$2 f + \frac{5}{3} + \frac{2}{3} (3 f) + \frac{2}{3} \cdot - 1 = \frac{4}{3} f$

Step 1.1.5

Cancel the common factor of $3$ .

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Step 1.1.5.1

Factor $3$ out of $3 f$ .

$2 f + \frac{5}{3} + \frac{2}{3} (3 (f)) + \frac{2}{3} \cdot - 1 = \frac{4}{3} f$

Step 1.1.5.2

Cancel the common factor.

$2 f + \frac{5}{3} + \frac{2}{3} (3 f) + \frac{2}{3} \cdot - 1 = \frac{4}{3} f$

Step 1.1.5.3

Rewrite the expression.

$2 f + \frac{5}{3} + 2 f + \frac{2}{3} \cdot - 1 = \frac{4}{3} f$

Step 1.1.6

Multiply $\frac{2}{3} \cdot - 1$ .

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Step 1.1.6.1

Combine $\frac{2}{3}$ and $- 1$ .

$2 f + \frac{5}{3} + 2 f + \frac{2 \cdot - 1}{3} = \frac{4}{3} f$

Step 1.1.6.2

Multiply $2$ by $- 1$ .

$2 f + \frac{5}{3} + 2 f + \frac{- 2}{3} = \frac{4}{3} f$

Step 1.1.7

Move the negative in front of the fraction.

$2 f + \frac{5}{3} + 2 f - \frac{2}{3} = \frac{4}{3} f$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$2 f + 2 f + \frac{5 - 2}{3} = \frac{4}{3} f$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Subtract $2$ from $5$ .

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

Step 1.2.2.2

Divide $3$ by $3$ .

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

Step 1.2.3

Add $2 f$ and $2 f$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{4 f}{3}$ from both sides of the equation.

$4 f + 1 - \frac{4 f}{3} = 0$

Step 3.2

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

$4 f \cdot \frac{3}{3} - \frac{4 f}{3} + 1 = 0$

Step 3.3

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

$\frac{4 f \cdot 3}{3} - \frac{4 f}{3} + 1 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{4 f \cdot 3 - 4 f}{3} + 1 = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $4 f$ out of $4 f \cdot 3 - 4 f$ .

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Step 3.5.1.1

Factor $4 f$ out of $4 f \cdot 3$ .

$\frac{4 f (3) - 4 f}{3} + 1 = 0$

Step 3.5.1.2

Factor $4 f$ out of $- 4 f$ .

$\frac{4 f (3) + 4 f (- 1)}{3} + 1 = 0$

Step 3.5.1.3

Factor $4 f$ out of $4 f (3) + 4 f (- 1)$ .

$\frac{4 f (3 - 1)}{3} + 1 = 0$

Step 3.5.2

Subtract $1$ from $3$ .

$\frac{4 f \cdot 2}{3} + 1 = 0$

Step 3.5.3

Multiply $2$ by $4$ .

$\frac{8 f}{3} + 1 = 0$

Step 4

Subtract $1$ from both sides of the equation.

$\frac{8 f}{3} = - 1$

Step 5

Multiply both sides of the equation by $\frac{3}{8}$ .

$\frac{3}{8} \cdot \frac{8 f}{3} = \frac{3}{8} \cdot - 1$

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 $\frac{3}{8} \cdot \frac{8 f}{3}$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8 f}{3} = \frac{3}{8} \cdot - 1$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 f) = \frac{3}{8} \cdot - 1$

Step 6.1.1.2

Cancel the common factor of $8$ .

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Step 6.1.1.2.1

Factor $8$ out of $8 f$ .

$\frac{1}{8} (8 (f)) = \frac{3}{8} \cdot - 1$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 f) = \frac{3}{8} \cdot - 1$

Step 6.1.1.2.3

Rewrite the expression.

$f = \frac{3}{8} \cdot - 1$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{3}{8} \cdot - 1$ .

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Step 6.2.1.1

Multiply $\frac{3}{8} \cdot - 1$ .

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Step 6.2.1.1.1

Combine $\frac{3}{8}$ and $- 1$ .

$f = \frac{3 \cdot - 1}{8}$

Step 6.2.1.1.2

Multiply $3$ by $- 1$ .

$f = \frac{- 3}{8}$

Step 6.2.1.2

Move the negative in front of the fraction.

$f = - \frac{3}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$f = - \frac{3}{8}$

Decimal Form:

$f = - 0.375$