Algebra Examples

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

Step 1

Simplify $3 - \frac{x + 7}{2}$ .

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Step 1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $3$ and $\frac{2}{2}$ .

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $3$ by $2$ .

$\frac{6 - (x + 7)}{2} = 9$

Step 1.3.2

Apply the distributive property.

$\frac{6 - x - 1 \cdot 7}{2} = 9$

Step 1.3.3

Multiply $- 1$ by $7$ .

$\frac{6 - x - 7}{2} = 9$

Step 1.3.4

Subtract $7$ from $6$ .

$\frac{- x - 1}{2} = 9$

Step 1.4

Simplify with factoring out.

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Step 1.4.1

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 1}{2} = 9$

Step 1.4.2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- (x) - 1 (1)}{2} = 9$

Step 1.4.3

Factor $- 1$ out of $- (x) - 1 (1)$ .

$\frac{- (x + 1)}{2} = 9$

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (x + 1)$ as $- 1 (x + 1)$ .

$\frac{- 1 (x + 1)}{2} = 9$

Step 1.4.4.2

Move the negative in front of the fraction.

$- \frac{x + 1}{2} = 9$

Step 2

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x + 1}{2}) = - 2 \cdot 9$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 2 (- \frac{x + 1}{2})$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{x + 1}{2}$ into the numerator.

$- 2 \frac{- (x + 1)}{2} = - 2 \cdot 9$

Step 3.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- (x + 1)}{2} = - 2 \cdot 9$

Step 3.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- (x + 1)}{2} = - 2 \cdot 9$

Step 3.1.1.1.4

Rewrite the expression.

$- - (x + 1) = - 2 \cdot 9$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (x + 1) = - 2 \cdot 9$

Step 3.1.1.2.2

Multiply $x + 1$ by $1$ .

$x + 1 = - 2 \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 2$ by $9$ .

$x + 1 = - 18$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$x = - 18 - 1$

Step 4.2

Subtract $1$ from $- 18$ .

$x = - 19$