Chapter 2: Q62. (page 108)

CHALLENGE Use the sentence $x = 7 \pm 4.6$ .
a. Describe the values of $(x)$ that make the sentence true.
b. Translate the sentence into an equation involving absolute value.

Short Answer

Expert verified

$x =11.6 and x =2.4$
$|x - 7| = 4.6$

Step by step solution

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:

$x =7\pm4.6 x = (7 +4.6) and x = (7 - 4.6) x =11.6 and x =2.4$

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

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

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

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:

$x =7\pm4.6 x = (7 +4.6) and x = (7 -4.6) x =11.6 and x =2.4$

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

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

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 $|x - 7| = 4.6$ .

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CHALLENGE Use the sentence $x = 7 \pm 4.6$ .
a. Describe the values of $(x)$ that make the sentence true.
b. Translate the sentence into an equation involving absolute value.

Short Answer

Step by step solution

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

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

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

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

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

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

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CHALLENGE Use the sentencex=7±4.6.a. Describe the values ofxthat make the sentence true.b. Translate the sentence into an equation involving absolute value.

Short Answer

Step by step solution

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

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

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

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

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Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

CHALLENGE Use the sentence $x = 7 \pm 4.6$ .
a. Describe the values of $(x)$ that make the sentence true.
b. Translate the sentence into an equation involving absolute value.