Algebra Examples

$\frac{7 x + 9}{5} - 12 = 8$

Step 1

Simplify $\frac{7 x + 9}{5} - 12$ .

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Step 1.1

To write $- 12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7 x + 9}{5} - 12 \cdot \frac{5}{5} = 8$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- 12$ and $\frac{5}{5}$ .

$\frac{7 x + 9}{5} + \frac{- 12 \cdot 5}{5} = 8$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{7 x + 9 - 12 \cdot 5}{5} = 8$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $- 12$ by $5$ .

$\frac{7 x + 9 - 60}{5} = 8$

Step 1.3.2

Subtract $60$ from $9$ .

$\frac{7 x - 51}{5} = 8$

Step 2

Multiply both sides by $5$ .

$\frac{7 x - 51}{5} \cdot 5 = 8 \cdot 5$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{7 x - 51}{5} \cdot 5 = 8 \cdot 5$

Step 3.1.1.2

Rewrite the expression.

$7 x - 51 = 8 \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $8$ by $5$ .

$7 x - 51 = 40$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $51$ to both sides of the equation.

$7 x = 40 + 51$

Step 4.1.2

Add $40$ and $51$ .

$7 x = 91$

Step 4.2

Divide each term in $7 x = 91$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = 91$ by $7$ .

$\frac{7 x}{7} = \frac{91}{7}$

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.

$\frac{7 x}{7} = \frac{91}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{91}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $91$ by $7$ .

$x = 13$