Finite Math Examples

$1 - \frac{7}{a} = 8$

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the equation.

$- \frac{7}{a} = 8 - 1$

Step 1.2

Subtract $1$ from $8$ .

$- \frac{7}{a} = 7$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$a, 1$

Step 2.2

The LCM of one and any expression is the expression.

$a$

Step 3

Multiply each term in $- \frac{7}{a} = 7$ by $a$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{7}{a} = 7$ by $a$ .

$- \frac{7}{a} a = 7 a$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{7}{a}$ into the numerator.

$\frac{- 7}{a} a = 7 a$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 7}{a} a = 7 a$

Step 3.2.1.3

Rewrite the expression.

$- 7 = 7 a$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $7 a = - 7$ .

$7 a = - 7$

Step 4.2

Divide each term in $7 a = - 7$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 a = - 7$ by $7$ .

$\frac{7 a}{7} = \frac{- 7}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{- 7}{7}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 7}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 7$ by $7$ .

$a = - 1$