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Chapter 0: Problem 68

Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 4 and 15

Short Answer

Expert verified
The absolute value expression for the distance between the numbers 4 and 15 is 11.

Step by step solution

01

Formulate the Absolute Value Expression

The absolute value of an expression involving two numbers \(a\) and \(b\) is formulated as \(|a - b|\). In this instance, the numbers are 4 and 15 and therefore the absolute value expression becomes \(|4 - 15|\).
02

Simplify the Expression Inside the Absolute Value

The inside of the absolute value is simplified first, so \(4 - 15 = -11\). The simplified absolute value expression becomes \(|-11|\).
03

Evaluate the Absolute Value Expression

The absolute value of a negative number is positive, so \(|-11|\) evaluates to 11.

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Most popular questions from this chapter

Simplify using properties of exponents. $$\left(7 x^{\frac{1}{3}}\right)\left(2 x^{\frac{1}{4}}\right)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{3}-64-(x+4)\left(x^{2}+4 x-16\right) $$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

Simplify by reducing the index of the radical. $$\sqrt[4]{7^{2}}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I use the definition for \(a^{\frac{m}{n}}\) I usually prefer lo first raise \(a\) to the \(m\) power because smaller numbers are involved.
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