Finite Math Examples

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

Step 1

Rewrite the equation as $\sqrt{2 - 3 x} = y$ .

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

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 - 3 x}}^{2} = y^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 - 3 x}$ as ${(2 - 3 x)}^{\frac{1}{2}}$ .

${({(2 - 3 x)}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(2 - 3 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(2 - 3 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 - 3 x)}^{1} = y^{2}$

Step 3.2.1.2

Simplify.

$2 - 3 x = y^{2}$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $2$ from both sides of the equation.

$- 3 x = y^{2} - 2$

Step 4.2

Divide each term in $- 3 x = y^{2} - 2$ by $- 3$ and simplify.

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Step 4.2.1

Divide each term in $- 3 x = y^{2} - 2$ by $- 3$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative in front of the fraction.

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

Step 4.2.3.1.2

Dividing two negative values results in a positive value.

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