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Chapter 7: Problem 43

Evaluate each expression if \(x=4\) and \(y=-1.\) $$y+6$$

Short Answer

Expert verified
The expression evaluates to 5.

Step by step solution

01

Substitute the variable

Replace the variable \(y\) in the expression \(y+6\) with the given value \(-1\) because \(y = -1\). This gives us: \((-1) + 6\).
02

Perform the addition

Now, add \(-1\) and \(6\) together. This results in \(-1 + 6 = 5\).

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Key Concepts

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

Substitution
Substitution is a fundamental technique in algebra, where you replace variables with their given values. This process is essential for solving expressions or equations. In the problem provided, we are given that \(x = 4\) and \(y = -1\). The expression requires us to evaluate \(y + 6\).
  • Identify the variable in the expression, which in this case is \(y\).
  • Replace \(y\) with its given value, \(-1\).
  • This process yields the expression \((-1) + 6\).
Substitution simplifies an expression, making it easy to perform further calculations.
Addition
Addition is one of the core arithmetic operations and is crucial when working with expressions involving numbers. Once substitution is done, the next step is to perform addition. Let's look at how this applies to the expression \((-1) + 6\).
  • Understand how to add numbers, especially when mixing a positive and a negative number.
  • Start with \(-1\) on the number line and move 6 units to the right.
  • This movement lands you at \(5\), which is the result of the addition.
Understanding addition helps in piecing together values post-substitution.
Integer Operations
Integer operations involve arithmetic using whole numbers, with special consideration for positive and negative values. In our example, \((-1) + 6\), you need to understand how these operations work:
  • Negative numbers move left on the number line, while positive numbers move right.
  • Adding a negative number is like moving backwards, and adding a positive number moves forward.
  • In the expression, we start at \(-1\) and add 6, moving right to end at \(5\).
Learning integer operations prepares you for handling more complex expressions with ease.

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Most popular questions from this chapter

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