Algebra Examples

$\sqrt{1 - x} - 6 y = 5$

Step 1

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

$- 6 y = 5 - \sqrt{1 - x}$

Step 2

Divide each term in $- 6 y = 5 - \sqrt{1 - x}$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 y = 5 - \sqrt{1 - x}$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{5}{- 6} + \frac{- \sqrt{1 - x}}{- 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{5}{- 6} + \frac{- \sqrt{1 - x}}{- 6}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{- 6} + \frac{- \sqrt{1 - x}}{- 6}$

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

Move the negative in front of the fraction.

$y = - \frac{5}{6} + \frac{- \sqrt{1 - x}}{- 6}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{5}{6} + \frac{\sqrt{1 - x}}{6}$

Step 2.3.2

Simplify terms.

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Step 2.3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 5 + \sqrt{1 - x}}{6}$

Step 2.3.2.2

Rewrite $- 5$ as $- 1 (5)$ .

$y = \frac{- 1 (5) + \sqrt{1 - x}}{6}$

Step 2.3.2.3

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

$y = \frac{- 1 (5) - 1 (- \sqrt{1 - x})}{6}$

Step 2.3.2.4

Factor $- 1$ out of $- 1 (5) - 1 (- \sqrt{1 - x})$ .

$y = \frac{- 1 (5 - \sqrt{1 - x})}{6}$

Step 2.3.2.5

Move the negative in front of the fraction.

$y = - \frac{5 - \sqrt{1 - x}}{6}$

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.

$f (x) = - \frac{5 - \sqrt{1 - x}}{6}$