Algebra Examples

$- \frac{7}{9} (x + 3) = 14$

Step 1

Multiply both sides of the equation by $- \frac{9}{7}$ .

$- \frac{9}{7} (- \frac{7}{9} \cdot (x + 3)) = - \frac{9}{7} \cdot 14$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{9}{7} (- \frac{7}{9} \cdot (x + 3))$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$- \frac{9}{7} (- \frac{7}{9} x - \frac{7}{9} \cdot 3) = - \frac{9}{7} \cdot 14$

Step 2.1.1.1.2

Combine $x$ and $\frac{7}{9}$ .

$- \frac{9}{7} (- \frac{x \cdot 7}{9} - \frac{7}{9} \cdot 3) = - \frac{9}{7} \cdot 14$

Step 2.1.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{7}{9}$ into the numerator.

$- \frac{9}{7} (- \frac{x \cdot 7}{9} + \frac{- 7}{9} \cdot 3) = - \frac{9}{7} \cdot 14$

Step 2.1.1.1.3.2

Factor $3$ out of $9$ .

$- \frac{9}{7} (- \frac{x \cdot 7}{9} + \frac{- 7}{3 (3)} \cdot 3) = - \frac{9}{7} \cdot 14$

Step 2.1.1.1.3.3

Cancel the common factor.

$- \frac{9}{7} (- \frac{x \cdot 7}{9} + \frac{- 7}{3 \cdot 3} \cdot 3) = - \frac{9}{7} \cdot 14$

Step 2.1.1.1.3.4

Rewrite the expression.

$- \frac{9}{7} (- \frac{x \cdot 7}{9} + \frac{- 7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Move $7$ to the left of $x$ .

$- \frac{9}{7} (- \frac{7 \cdot x}{9} + \frac{- 7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$- \frac{9}{7} (- \frac{7 x}{9} - \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

Apply the distributive property.

$- \frac{9}{7} (- \frac{7 x}{9}) - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.2

Cancel the common factor of $9$ .

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Step 2.1.1.3.2.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

$\frac{- 9}{7} (- \frac{7 x}{9}) - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.2.2

Move the leading negative in $- \frac{7 x}{9}$ into the numerator.

$\frac{- 9}{7} \cdot \frac{- 7 x}{9} - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.2.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{7} \cdot \frac{- 7 x}{9} - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.2.4

Cancel the common factor.

$\frac{9 \cdot - 1}{7} \cdot \frac{- 7 x}{9} - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.2.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.3.1

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.3.3

Rewrite the expression.

$- - x - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.4

Multiply.

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Step 2.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.4.2

Multiply $x$ by $1$ .

$x - \frac{9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.5

Cancel the common factor of $3$ .

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Step 2.1.1.3.5.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

$x + \frac{- 9}{7} (- \frac{7}{3}) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.5.2

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$x + \frac{- 9}{7} \cdot \frac{- 7}{3} = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.5.3

Factor $3$ out of $- 9$ .

$x + \frac{3 (- 3)}{7} \cdot \frac{- 7}{3} = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.5.4

Cancel the common factor.

$x + \frac{3 \cdot - 3}{7} \cdot \frac{- 7}{3} = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.5.5

Rewrite the expression.

$x + \frac{- 3}{7} \cdot - 7 = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.6

Cancel the common factor of $7$ .

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Step 2.1.1.3.6.1

Factor $7$ out of $- 7$ .

$x + \frac{- 3}{7} \cdot (7 (- 1)) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.6.2

Cancel the common factor.

$x + \frac{- 3}{7} \cdot (7 \cdot - 1) = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.6.3

Rewrite the expression.

$x - 3 \cdot - 1 = - \frac{9}{7} \cdot 14$

Step 2.1.1.3.7

Multiply $- 3$ by $- 1$ .

$x + 3 = - \frac{9}{7} \cdot 14$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{9}{7} \cdot 14$ .

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Step 2.2.1.1

Cancel the common factor of $7$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

$x + 3 = \frac{- 9}{7} \cdot 14$

Step 2.2.1.1.2

Factor $7$ out of $14$ .

$x + 3 = \frac{- 9}{7} \cdot (7 (2))$

Step 2.2.1.1.3

Cancel the common factor.

$x + 3 = \frac{- 9}{7} \cdot (7 \cdot 2)$

Step 2.2.1.1.4

Rewrite the expression.

$x + 3 = - 9 \cdot 2$

Step 2.2.1.2

Multiply $- 9$ by $2$ .

$x + 3 = - 18$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$x = - 18 - 3$

Step 3.2

Subtract $3$ from $- 18$ .

$x = - 21$