Q62. - Algebra 1

Question

CHALLENGE Use the sentence $\mathbf{x}\mathbf{=}\mathbf{7}\mathbf{\pm }\mathbf{4}\mathbf{.}\mathbf{6}$.

a. Describe the values of $\left(x\right)$ that make the sentence true.

b. Translate the sentence into an equation involving absolute value.

Step-by-Step Solution

Answer

1. $x = 11.6\text{ and }x = 2.4$
   
2. $\left|x-7\right|=4.6$
   

Part a. Step 1. Write down the given statement.

It is given that,

$x=7\pm 4.6$

Part a. Step 2. Evaluate (x) from the given expression.

The values of x can be evaluated as:

$$\begin{gathered} x=7\pm 4.6 \\ x=\left(7+4.6\right) \text{and} x=\left(7-4.6\right) \\ x=11.6 \text{and} x=2.4 \end{gathered}$$

Therefore, the values of x for which the given sentence is true are $x=11.6\text{ and }x=2.4$.

Part a. Step 3. Conclusion from the obtained value of (x).

From the obtained values, the expression is true for $x=11.6 \text{and} x=2.4$.

Part b. Step 1. Write down the given statement.

The given statement is:

$x=7\pm 4.6$

Part b. Step 2. Evaluate (x) and determine mid-point from the obtained values of (x) by taking average.

The values of $x$ can be described as:

$$\begin{gathered} x=7\pm 4.6 \\ x=\left(7+4.6\right) \text{and} x=\left(7-4.6\right) \\ x=11.6 \text{and} x=2.4 \end{gathered}$$

First, we will find the average of the two given points, i.e. 2.4 and 11.6 to find the mid-point.

$$\begin{gathered} =\frac{2.4+11.6}{2} \\ =\frac{14}{2} \\ =7 \end{gathered}$$

Part b. Step 3. Write the equation for the expression.

The distance from 2.4 to 7 is 4.6 units and the distance from 7 to 11.6 is also 4.6 units.

So, the equation will be $\left|x-7\right|=4.6$.