Algebra Examples

$3 \cdot 1 = \frac{72}{f} - 5$

Step 1

Rewrite the equation as $\frac{72}{f} - 5 = 3 \cdot 1$ .

$\frac{72}{f} - 5 = 3 \cdot 1$

Step 2

Multiply $3$ by $1$ .

$\frac{72}{f} - 5 = 3$

Step 3

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

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Step 3.1

Add $5$ to both sides of the equation.

$\frac{72}{f} = 3 + 5$

Step 3.2

Add $3$ and $5$ .

$\frac{72}{f} = 8$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$f, 1$

Step 4.2

The LCM of one and any expression is the expression.

$f$

Step 5

Multiply each term in $\frac{72}{f} = 8$ by $f$ to eliminate the fractions.

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Step 5.1

Multiply each term in $\frac{72}{f} = 8$ by $f$ .

$\frac{72}{f} f = 8 f$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $f$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{72}{f} f = 8 f$

Step 5.2.1.2

Rewrite the expression.

$72 = 8 f$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $8 f = 72$ .

$8 f = 72$

Step 6.2

Divide each term in $8 f = 72$ by $8$ and simplify.

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Step 6.2.1

Divide each term in $8 f = 72$ by $8$ .

$\frac{8 f}{8} = \frac{72}{8}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $8$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{8 f}{8} = \frac{72}{8}$

Step 6.2.2.1.2

Divide $f$ by $1$ .

$f = \frac{72}{8}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $72$ by $8$ .

$f = 9$