Algebra Examples

$- \frac{1}{5} f + 8 = \frac{3}{5} (\frac{5}{3} f + 15) - \frac{1}{5} f$

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.

$\frac{3}{5} \cdot (\frac{5}{3} f + 15) - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2

Simplify $\frac{3}{5} \cdot (\frac{5}{3} f + 15) - \frac{1}{5} f$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{3}{5} \cdot (\frac{5 f}{3} + 15) - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.2

Apply the distributive property.

$\frac{3}{5} \cdot \frac{5 f}{3} + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 f}{3} + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.3.2

Rewrite the expression.

$\frac{1}{5} (5 f) + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.4

Cancel the common factor of $5$ .

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Step 2.1.4.1

Factor $5$ out of $5 f$ .

$\frac{1}{5} (5 (f)) + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.4.2

Cancel the common factor.

$\frac{1}{5} (5 f) + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.4.3

Rewrite the expression.

$f + \frac{3}{5} \cdot 15 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.5

Cancel the common factor of $5$ .

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Step 2.1.5.1

Factor $5$ out of $15$ .

$f + \frac{3}{5} \cdot (5 (3)) - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.5.2

Cancel the common factor.

$f + \frac{3}{5} \cdot (5 \cdot 3) - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.5.3

Rewrite the expression.

$f + 3 \cdot 3 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.6

Multiply $3$ by $3$ .

$f + 9 - \frac{1}{5} f = - \frac{1}{5} f + 8$

Step 2.1.7

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

$f + 9 - \frac{f}{5} = - \frac{1}{5} f + 8$

Step 2.2

To write $f$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$f \cdot \frac{5}{5} - \frac{f}{5} + 9 = - \frac{1}{5} f + 8$

Step 2.3

Combine $f$ and $\frac{5}{5}$ .

$\frac{f \cdot 5}{5} - \frac{f}{5} + 9 = - \frac{1}{5} f + 8$

Step 2.4

Combine the numerators over the common denominator.

$\frac{f \cdot 5 - f}{5} + 9 = - \frac{1}{5} f + 8$

Step 2.5

Subtract $f$ from $f \cdot 5$ .

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Step 2.5.1

Reorder $f$ and $5$ .

$\frac{5 \cdot f - f}{5} + 9 = - \frac{1}{5} f + 8$

Step 2.5.2

Subtract $f$ from $5 \cdot f$ .

$\frac{4 \cdot f}{5} + 9 = - \frac{1}{5} f + 8$

$\frac{4 f}{5} + 9 = - \frac{1}{5} f + 8$

Step 3

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

$\frac{4 f}{5} + 9 = - \frac{f}{5} + 8$

Step 4

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

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Step 4.1

Add $\frac{f}{5}$ to both sides of the equation.

$\frac{4 f}{5} + 9 + \frac{f}{5} = 8$

Step 4.2

Combine the numerators over the common denominator.

$9 + \frac{4 f + f}{5} = 8$

Step 4.3

Add $4 f$ and $f$ .

$9 + \frac{5 f}{5} = 8$

Step 4.4

Cancel the common factor of $5$ .

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Step 4.4.1

Cancel the common factor.

$9 + \frac{5 f}{5} = 8$

Step 4.4.2

Divide $f$ by $1$ .

$9 + f = 8$

Step 5

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

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Step 5.1

Subtract $9$ from both sides of the equation.

$f = 8 - 9$

Step 5.2

Subtract $9$ from $8$ .

$f = - 1$