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Chapter 1: Problem 6

Evaluate. $$|6|-8$$

Short Answer

Expert verified
-2

Step by step solution

01

Evaluate the absolute value

Evaluate \(|6|\). Since 6 is a positive number, its absolute value is itself, so \(|6| = 6\).
02

Perform the subtraction

Now substitute \(|6|\) with 6 in the expression, which gives us \(6 - 8\). Subtract 8 from 6, which results in -2.

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Key Concepts

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

Positive Numbers
Positive numbers are values greater than zero. They are located to the right of zero on the number line. In the world of mathematics, positive numbers play a crucial role because they generally represent quantities that can be counted.

When evaluating expressions involving positive numbers in absolute value, it is essential to remember that the absolute value of a positive number is the number itself. The symbol for absolute value is "| |," and it measures how far a number is from zero regardless of direction.
  • Example: The absolute value of 6 is 6, written as \(|6| = 6\).
  • This concept simplifies the process of evaluating expressions since for any positive number, taking its absolute value doesn't change its value.
Subtraction
Subtraction is one of the basic arithmetic operations allowing us to find the difference between two numbers. It can be thought of as "taking away" one number from another.

In math, the operation is represented by the minus sign "-". Subtracting a larger number from a smaller one, as in our expression \(6 - 8\), yields a negative result. The first number in a subtraction sequence is called the minuend, and the second number is the subtrahend.
  • For the example \(6 - 8\), 6 is the minuend, and 8 is the subtrahend.
  • The calculation \(6 - 8 = -2\) shows how a number can become negative when a larger number is subtracted from a smaller one.
Evaluate Expressions
Evaluating expressions means performing the operations indicated in an expression and simplifying it to a single value or completed form.

For our example expression \(|6| - 8\), we need to evaluate the absolute value first. This is a common step in math problems where simplification leads you to perform sequential calculations.

Here's a simplified way to evaluate such expressions:
  • Step 1: Evaluate any absolute values. For \(|6|\), it remains 6 because it is positive.
  • Step 2: Substitute back into the expression and perform other operations, like subtraction. Thus \(6 - 8 = -2\).
By following these sequential steps, you'll effectively break down and solve expressions without missing key details, making complex problems much simpler to solve.

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Most popular questions from this chapter

Let \(F\) be defined as follows. $$F(x)=\left\\{\begin{array}{ll}x, & \text { if } 0 \leq x \leq 4 \\\4, & \text { if } x>4\end{array}\right.$$ Graph \(F(2 x)\)

What happens when you graph \(y=x+100\) in the standard viewing window of your graphing utility? How can you change the window so that you can see a clearer graph?

Solve the inequality. Express your answer in interval notation. $$-2 x-1 \geq \frac{x+5}{2}$$

Graph the piecewise-defined function using a graphing utility. The display should be in DOT mode. $$f(x)=\left\\{\begin{array}{ll} x^{2}, & \text { if }-2 \leq x<0 \\ -x+1, & \text { if } 0 \leq x<2.5 \\ x-3.5, & \text { if } x \geq 2.5 \end{array}\right.$$

Applications In this set of exercises you will use the concepts of intersection of lines and linear inequalities to study real-world problems. Cost and Revenue In Exercises \(69-72,\) for each set of cost and revenue functions, (a) find the break-even point and (b) calculate the values of \(q\) for cohich retucnue exceeds cost. $$\begin{aligned} &C(q)=10 q+200\\\ &R(q)=15 q \end{aligned}$$
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