Algebra Examples

$y = 5 {(\frac{1}{2})}^{x} - 3$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = 5 {(\frac{1}{2})}^{- 2} - 3$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{- 2} - 3$

Step 2.2

Simplify $5 {(\frac{1}{2})}^{- 2} - 3$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 5 \cdot 2^{2} - 3$

Step 2.2.1.2

Raise $2$ to the power of $2$ .

$y = 5 \cdot 4 - 3$

Step 2.2.1.3

Multiply $5$ by $4$ .

$y = 20 - 3$

Step 2.2.2

Subtract $3$ from $20$ .

$y = 17$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = 5 {(\frac{1}{2})}^{- 1} - 3$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{- 1} - 3$

Step 4.2

Simplify $5 {(\frac{1}{2})}^{- 1} - 3$ .

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 5 \cdot 2 - 3$

Step 4.2.1.2

Multiply $5$ by $2$ .

$y = 10 - 3$

Step 4.2.2

Subtract $3$ from $10$ .

$y = 7$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = 5 {(\frac{1}{2})}^{0} - 3$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{0} - 3$

Step 6.2

Simplify $5 {(\frac{1}{2})}^{0} - 3$ .

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Apply the product rule to $\frac{1}{2}$ .

$y = 5 \frac{1^{0}}{2^{0}} - 3$

Step 6.2.1.2

Anything raised to $0$ is $1$ .

$y = 5 \frac{1}{2^{0}} - 3$

Step 6.2.1.3

Anything raised to $0$ is $1$ .

$y = 5 (\frac{1}{1}) - 3$

Step 6.2.1.4

Cancel the common factor of $1$ .

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Step 6.2.1.4.1

Cancel the common factor.

$y = 5 (\frac{1}{1}) - 3$

Step 6.2.1.4.2

Rewrite the expression.

$y = 5 \cdot 1 - 3$

Step 6.2.1.5

Multiply $5$ by $1$ .

$y = 5 - 3$

Step 6.2.2

Subtract $3$ from $5$ .

$y = 2$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = 5 {(\frac{1}{2})}^{1} - 3$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 5 (\frac{1}{2}) - 3$

Step 8.2

Simplify $5 (\frac{1}{2}) - 3$ .

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Step 8.2.1

Combine $5$ and $\frac{1}{2}$ .

$y = \frac{5}{2} - 3$

Step 8.2.2

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

$y = \frac{5}{2} - 3 \cdot \frac{2}{2}$

Step 8.2.3

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

$y = \frac{5}{2} + \frac{- 3 \cdot 2}{2}$

Step 8.2.4

Combine the numerators over the common denominator.

$y = \frac{5 - 3 \cdot 2}{2}$

Step 8.2.5

Simplify the numerator.

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Step 8.2.5.1

Multiply $- 3$ by $2$ .

$y = \frac{5 - 6}{2}$

Step 8.2.5.2

Subtract $6$ from $5$ .

$y = \frac{- 1}{2}$

Step 8.2.6

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = 5 {(\frac{1}{2})}^{2} - 3$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{2} - 3$

Step 10.2

Simplify $5 {(\frac{1}{2})}^{2} - 3$ .

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Step 10.2.1

Simplify each term.

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Step 10.2.1.1

Apply the product rule to $\frac{1}{2}$ .

$y = 5 \frac{1^{2}}{2^{2}} - 3$

Step 10.2.1.2

One to any power is one.

$y = 5 \frac{1}{2^{2}} - 3$

Step 10.2.1.3

Raise $2$ to the power of $2$ .

$y = 5 (\frac{1}{4}) - 3$

Step 10.2.1.4

Combine $5$ and $\frac{1}{4}$ .

$y = \frac{5}{4} - 3$

Step 10.2.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{5}{4} - 3 \cdot \frac{4}{4}$

Step 10.2.3

Combine $- 3$ and $\frac{4}{4}$ .

$y = \frac{5}{4} + \frac{- 3 \cdot 4}{4}$

Step 10.2.4

Combine the numerators over the common denominator.

$y = \frac{5 - 3 \cdot 4}{4}$

Step 10.2.5

Simplify the numerator.

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Step 10.2.5.1

Multiply $- 3$ by $4$ .

$y = \frac{5 - 12}{4}$

Step 10.2.5.2

Subtract $12$ from $5$ .

$y = \frac{- 7}{4}$

Step 10.2.6

Move the negative in front of the fraction.

$y = - \frac{7}{4}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 17 \\ - 1 & 7 \\ 0 & 2 \\ 1 & - \frac{1}{2} \\ 2 & - \frac{7}{4} \end{array}$

Step 12