Algebra Examples

$\sqrt{1 - x} + 2 y = - 6$

Step 1

Subtract $\sqrt{1 - x}$ from both sides of the equation.

$2 y = - 6 - \sqrt{1 - x}$

Step 2

Divide each term in $2 y = - 6 - \sqrt{1 - x}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = - 6 - \sqrt{1 - x}$ by $2$ .

$\frac{2 y}{2} = \frac{- 6}{2} + \frac{- \sqrt{1 - x}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 6}{2} + \frac{- \sqrt{1 - x}}{2}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6}{2} + \frac{- \sqrt{1 - x}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 6$ by $2$ .

$y = - 3 + \frac{- \sqrt{1 - x}}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - 3 - \frac{\sqrt{1 - x}}{2}$

Step 2.3.2

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

$y = - 3 \cdot \frac{2}{2} - \frac{\sqrt{1 - x}}{2}$

Step 2.3.3

Simplify terms.

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Step 2.3.3.1

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

$y = \frac{- 3 \cdot 2}{2} - \frac{\sqrt{1 - x}}{2}$

Step 2.3.3.2

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 2 - \sqrt{1 - x}}{2}$

Step 2.3.4

Simplify the numerator.

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Step 2.3.4.1

Factor $- 1$ out of $- 3 \cdot 2 - \sqrt{1 - x}$ .

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Step 2.3.4.1.1

Reorder $1$ and $- x$ .

$y = \frac{- 3 \cdot 2 - \sqrt{- x + 1}}{2}$

Step 2.3.4.1.2

Factor $- 1$ out of $- 3 \cdot 2$ .

$y = \frac{- (3 \cdot 2) - \sqrt{- x + 1}}{2}$

Step 2.3.4.1.3

Factor $- 1$ out of $- \sqrt{- x + 1}$ .

$y = \frac{- (3 \cdot 2) - (\sqrt{- x + 1})}{2}$

Step 2.3.4.1.4

Factor $- 1$ out of $- (3 \cdot 2) - (\sqrt{- x + 1})$ .

$y = \frac{- (3 \cdot 2 + \sqrt{- x + 1})}{2}$

Step 2.3.4.2

Multiply $3$ by $2$ .

$y = \frac{- (6 + \sqrt{- x + 1})}{2}$

Step 2.3.5

Move the negative in front of the fraction.

$y = - \frac{6 + \sqrt{- x + 1}}{2}$

Step 3

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{6 + \sqrt{- x + 1}}{2}$