169k views
3 votes
The values of x shown on the number line below are solutions to an absolute valueequation.

User Graphileon
by
8.4k points

1 Answer

3 votes

We will use the solutions to the absolute value functions to determine the function's description as follows:

The two solutions to the absolute value function are given as follows:


x\text{ = -3 and x = 5}

We will investigate each description as follows:

A) The distance of x from -3 is 8.

We will use the number line and determine the distance from ( x = -3 ) to the other solution ( x = 5 ). The number of units along the x-axis from point ( x = -3 ) to ( x = 5 ) would be:


\textcolor{#FF7968}{8}\text{\textcolor{#FF7968}{ units}}

Hence, option A is correct!

B) This option describes the absolute value function as follows:


|\text{ x }-\text = 5

We will solve the above absolute value function as follows:


\begin{gathered} +(x\text{ - 3 ) = 5 OR -(x - 3 ) = 5} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 8 }}\text{ OR }\text{\textcolor{#FF7968}{x = -2}} \end{gathered}

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option B is incorrect!

C) The distance of x from 1 is 4

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 1 ) as follows:


\text{\textcolor{#FF7968}{Distance}}\text{ = 5 - 1 = 1 - ( - 3 ) = 4}

We see that the distance from each solution ( x = -3 ) AND ( x = 5 ) from point ( x = 1 ) is 4 units along the x axis. Hence, option C is correct!

D) The distance of x from 4 is 1

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:


\begin{gathered} \text{Distance : ( x = 5 ) - ( x = 4 ) = }\text{\textcolor{#FF7968}{1 unit}} \\ \text{Distance : ( x = -3 ) - ( x = 4 ) = }\text{\textcolor{#FF7968}{7 units}} \end{gathered}

The above statement is true for the solution ( x = 5 ); however, incorrect for solution ( x = -3 ). Hence, we will reject this option D as it is not true in entirety!

E) This option describes the absolute value function as follows:


|\text{ x }-\text 4 1

We will solve the above absolute value function as follows:


\begin{gathered} +(x\text{ - 4 ) = 1 OR - ( x - 4 ) = }1 \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 5 }}\text{ OR }\text{\textcolor{#FF7968}{x = }}\textcolor{#FF7968}{3} \end{gathered}

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option E is incorrect!

F) This option describes the absolute value function as follows:


|\text x + 1 4

We will solve the above absolute value function as follows:


\begin{gathered} +(x\text{ + 1 ) = 4 OR - ( x + 1 ) = }4 \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 3 }}\text{ OR }\text{\textcolor{#FF7968}{x = -}}\textcolor{#FF7968}{3} \end{gathered}

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option F is incorrect!

G) The distance of x from -3 is 5

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:


\begin{gathered} \text{Distance : ( x = 5 ) - ( x = -3 ) = }\text{\textcolor{#FF7968}{8 unit}} \\ \end{gathered}

The above statement is not true for the solution ( x = 5 ). Hence, we will reject this option G as it is not true in entirety!

H) This option describes the absolute value function as follows:


|\text{ x }-\text 1 4

We will solve the above absolute value function as follows:


\begin{gathered} +(x\text{ - 1 ) = 4 OR - ( x - 1 ) = }4 \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 5 }}\text{ OR }\text{\textcolor{#FF7968}{x = -}}\textcolor{#FF7968}{3} \end{gathered}

The above solution to the absolute value function is equal to the solution presented in the number line. Hence, option H is correct!

The correct statements are:


\textcolor{#FF7968}{A}\text{\textcolor{#FF7968}{ , C , H}}

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:


undefined

User Atul Gupta
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories