Question

In Problems 49-58, find the value of each expression if \(x=3\) and \(y=-2\). \(|x|+|y|\)

Short answer

5

Step-by-step solution

Understand Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always a non-negative number.

Substitute Values

Substitute the given values into the expression: Substitute \(x = 3\) and \(y = -2\) into \(|x|+|y|\).

Calculate Absolute Values

Calculate the absolute values of \(x\) and \(y\): \(|x| = |3| = 3\)\(|y| = |-2| = 2\)

Add the Absolute Values

Add the absolute values from the previous step: \(3 + 2 = 5\)

Key concepts

absolute value

Absolute value is an important concept in mathematics. It tells us how far a number is from zero on the number line, without considering if it's positive or negative.
For example, both 3 and -3 have an absolute value of 3, as they are each 3 units away from zero.
The notation for absolute value is two vertical bars around the number, like this: \(|x|\).
Whenever we see this notation, it means we should ignore the sign and only focus on the number's distance from zero.
To summarize, the absolute value of a number is always non-negative. That means it's either positive or zero.

substitution in expressions

Substitution in expressions is a technique used to replace variables with actual values. This helps us evaluate the expression.
Let's say we have an expression with variables, like \(|x| + |y|\), and we are given specific values for \(x\) and \(y\).
For instance, if \(x = 3\) and \(y = -2\), we substitute these values into the expression to replace \(x\) and \(y\).
Our expression becomes \(|3| + |-2|\).

basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These are the foundational operations in algebra.
For this exercise, we focus on addition. After calculating the absolute values, we need to add them together.
In our example, after finding that \(|3| = 3\) and \(|-2| = 2\), we add these results together.
Thus, \(|3| + |-2| = 3 + 2 = 5\).
Understanding these basic operations is crucial as they form the building blocks for more complex mathematics.