Pre-Algebra Examples

$y = 2 x - 8$

Step 1

Write $y = 2 x - 8$ as a function.

$f (x) = 2 x - 8$

Step 2

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.

Largest Degree: $1$

Leading Coefficient: $2$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$f (x) = \frac{2 x}{2} + \frac{- 8}{2}$

Step 3.1.2

Divide $x$ by $1$ .

$f (x) = x + \frac{- 8}{2}$

Step 3.2

Divide $- 8$ by $2$ .

$f (x) = x - 4$

Step 4

Create a list of the coefficients of the function except the leading coefficient of $1$ .

$- 4$

Step 5

There will be two bound options, $b_{1}$ and $b_{2}$ , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add $1$ .

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Step 5.1

Arrange the terms in ascending order.

$b_{1} = | - 4 |$

Step 5.2

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$b_{1} = 4 + 1$

Step 5.3

Add $4$ and $1$ .

$b_{1} = 5$

Step 6

To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than $1$ , use that number. If not, use $1$ .

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Step 6.1

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$b_{2} = 4$

Step 6.2

Arrange the terms in ascending order.

$b_{2} = 1, 4$

Step 6.3

The maximum value is the largest value in the arranged data set.

$b_{2} = 4$

Step 7

Take the smaller bound option between $b_{1} = 5$ and $b_{2} = 4$ .

Smaller Bound: $4$

Step 8

Every real root on $f (x) = 2 x - 8$ lies between $- 4$ and $4$ .

$- 4$ and $4$