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Chapter 1: Problem 9

Select the point on the number line that corresponds to \(|Q-R|-T\). (For this practice test, mark the point with an X.)

Short Answer

Expert verified
To find the point on the number line that corresponds to \(|Q-R|-T\), follow these steps: 1. Determine the values of Q, R, and T on the number line. 2. Calculate the difference between Q and R: \(Q - R\). 3. Find the absolute value of the difference: \(|Q - R|\). 4. Subtract T from the absolute value: \(|Q - R| - T\). 5. Locate and mark the point corresponding to the final value on the number line with an X.

Step by step solution

01

Understand the concept of absolute value

The absolute value of a number is the distance between that number and 0 on the number line. It's always a non-negative value. For example, the absolute value of -3 is 3, and the absolute value of 5 is also 5.
02

Identify the values of Q, R, and T

Determine the values of Q, R, and T on the number line. Find the number corresponding to each point, and make sure you understand their locations in relation to one another.
03

Calculate the difference between Q and R

Now, you need to find the difference between the values of Q and R. To do this, subtract the smaller number from the larger one. For example, if Q was at 5 and R was at -2, the difference would be: \(Q - R = 5 - (-2) = 5 + 2 = 7\)
04

Find the absolute value of the difference

In the previous step, you found the difference between Q and R. Now, you need to find the absolute value of that difference. Recall that the absolute value is the distance of a number from 0. Using the previous example: \(|Q - R| = |7| = 7\)
05

Subtract T from the absolute value

Now that you have found the absolute value of the difference between Q and R, you need to subtract T from it. Let's say T was at -3, then the subtraction would look like this: \(|Q - R| - T = 7 - (-3) = 7 + 3 = 10\)
06

Locate the final value on the number line

After finding the value of \(|Q-R|-T\), locate this value on the number line. Start at zero, then mark the point corresponding to the value you found in step 5. In our example, locate the point at 10 and mark it with an X.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

GED Math Practice
GED Math can seem daunting, but with the right practice, it's highly manageable. One area to focus on is number line operations, which often involve absolute values. It's not just about solving an equation; it's about visualizing numbers in space. This sensory approach to mathematics often makes it easier to grasp.

When confronted with an absolute value calculation, picture the number line in your mind. Imagine walking along it as you perform each operation. This not only aids in understanding but also prepares you for test day, as the GED exam will likely include similar problems. Always remember, GED Math practice should be consistent, and engaging with exercises such as number line operations strengthens your mental math muscles.
Absolute Value Calculation
Understanding absolute values is crucial for many mathematical concepts, including GED math. An absolute value reflects how far a number is from zero, representing its magnitude regardless of its direction on the number line. To calculate it, simply consider the distance without regard for whether the number is positive or negative.

For instance, both \( -4 \) and \( 4 \) have an absolute value of \( 4 \) because they are the same distance from zero, just in opposite directions. Learning to quickly find the absolute value will save time and boost your confidence in more complex mathematical tasks within the GED curriculum.
Number Line Operations
Number lines are not only tools for counting; they're fundamental in understanding more advanced operations. When calculating the result of \( |Q-R|-T \) like in our exercise, you're performing a series of operations visualized on this line.

Firstly, find the positions of \( Q \) and \( R \) and then consider their difference as a distance. After that, take the absolute value, which essentially 'flips' any negative result into the positive zone. Finally, introducing the variable \( T \) into your calculation, adjust your position accordingly. Through consistent practice of such number line operations, complex problems can soon become intuitive.

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