Pre-Algebra Examples

$P (x) = 3 - 0.7 x$

Step 1

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

Largest Degree: $1$

Leading Coefficient: $- 0.7$

Step 2

Simplify each term.

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Step 2.1

Divide $3$ by $- 0.7$ .

$P (x) = - 4.\overline{285714} + \frac{- 0.7 x}{- 0.7}$

Step 2.2

Cancel the common factor of $- 0.7$ .

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Step 2.2.1

Cancel the common factor.

$P (x) = - 4.\overline{285714} + \frac{- 0.7 x}{- 0.7}$

Step 2.2.2

Divide $x$ by $1$ .

$P (x) = - 4.\overline{285714} + x$

Step 3

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

$- 4.\overline{285714}$

Step 4

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 4.1

Arrange the terms in ascending order.

$b_{1} = | - 4.\overline{285714} |$

Step 4.2

The absolute value is the distance between a number and zero. The distance between $- 4.\overline{285714}$ and $0$ is $4.\overline{285714}$ .

$b_{1} = 4.\overline{285714} + 1$

Step 4.3

Add $4.\overline{285714}$ and $1$ .

$b_{1} = 5.\overline{285714}$

Step 5

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 5.1

The absolute value is the distance between a number and zero. The distance between $- 4.\overline{285714}$ and $0$ is $4.\overline{285714}$ .

$b_{2} = 4.\overline{285714}$

Step 5.2

Arrange the terms in ascending order.

$b_{2} = 1, 4.\overline{285714}$

Step 5.3

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

$b_{2} = 4.\overline{285714}$

Step 6

Take the smaller bound option between $b_{1} = 5.\overline{285714}$ and $b_{2} = 4.\overline{285714}$ .

Smaller Bound: $4.\overline{285714}$

Step 7

Every real root on $P (x) = 3 - 0.7 x$ lies between $- 4.\overline{285714}$ and $4.\overline{285714}$ .

$- 4.\overline{285714}$ and $4.\overline{285714}$