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Chapter 2: Problem 29

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x+y$$

Short Answer

Expert verified
The value of the expression is $$-1.$$

Step by step solution

01

Understand the Expression

The given expression is $$x + y.$$
02

Substitute the Given Values

Substitute the values of the variables into the expression:$$x = 2 \text{ and } y = -3.$$
03

Perform the Addition

Now add the values:$$2 + (-3) = -1.$$

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Key Concepts

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

substitution
Substitution means replacing variables in an expression with their given numerical values. In this exercise, we are given values for the variables:
  • x = 2
  • y = -3

To evaluate the expression, we need to substitute the given values into it.
For example, the expression is x + y. After substituting the values, the expression becomes 2 + (-3). This first step is crucial because it transforms an abstract expression into a concrete arithmetic problem that we can solve.
addition
Addition is the process of finding the total, or sum, by combining two or more numbers. In our exercise, we need to add 2 and -3. Remember, when you're adding a positive number and a negative number, you are essentially finding the difference between the two numbers and keeping the sign of the larger number.
For example in our case:
  • 2 is positive.
  • -3 is negative.

When we add these, we perform the arithmetic: (2) + (-3) = -1. Notice that when you add 2 and -3, it鈥檚 like subtracting 3 from 2. That gives us -1 because the negative number (3) is larger in absolute terms than the positive number (2).
integer arithmetic
Integer arithmetic involves performing operations such as addition, subtraction, multiplication, and division with integers. Integers include positive numbers, negative numbers, and zero. Let's focus on addition for now:
  • Adding two positive integers gives a positive result: 2 + 3 = 5.
  • Adding two negative integers gives a negative result: (-2) + (-3) = -5.
  • Adding a positive integer and a negative integer: 2 + (-3) = -1.

Our exercise is already using integer arithmetic with a positive integer (2) and a negative integer (-3). Understanding how to work with positive and negative integers is essential for evaluating expressions accurately in various math problems.

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Most popular questions from this chapter

Simplify each expression as completely as possible. $$7(a-1)-6[2 a-4(a-3)]$$

Simplify by combining like terms whenever possible. $$5 x^{2} y-3 x^{2}+x^{2} y-x^{2}$$

Simplify by combining like terms whenever possible. $$0.06 x+0.09(x+5,000)$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(y-2 z)(y+3 z)$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$5 x^{2}-2 x y^{2}+z x^{2} y$$
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