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Chapter 2: Problem 48

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

Short Answer

Expert verified
9.

Step by step solution

01

- Substitute the Values

Substitute the given values of the variables into the expression. The expression is x-(y+z). With the given values, it becomes 2-(-3+(-4)).
02

- Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: -3 + (-4). Adding these values together, we get -3 - 4 = -7.
03

- Perform the Subtraction

Now subtract -7 from 2: 2 - (-7). Remember that subtracting a negative number is the same as adding the positive equivalent, so this becomes 2 + 7.
04

- Calculate the Final Answer

Add the numbers: 2 + 7 = 9.

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Key Concepts

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

Variable Substitution
Variable substitution is the process of replacing variables in an expression with their given numerical values. Imagine you're handed the expression \(x - (y + z)\) and told that \(x = 2\), \(y = -3\), and \(z = -4\). The first step in variable substitution is to replace each variable with these values. So, the expression \(x - (y + z)\) becomes \(2 - (-3 + (-4))\). This step is crucial because it sets the stage for simplifying the expression. Be sure to replace each variable accurately to avoid mistakes later on.
Simplify Expressions
Once you've substituted the variables, the next step is to simplify the expression. Simplifying involves combining like terms and performing any operations inside parentheses first. In our example \(2 - (-3 + (-4))\), start by simplifying inside the parentheses. Here, you add \(-3\) and \(-4\), which yields \(-7\). So the expression now looks like \(2 - (-7)\). Simplifying makes expressions easier to understand and work with, helping you see the problem more clearly.
Negative Numbers
Handling negative numbers can be tricky, but with practice, it becomes easier. Negative numbers are numbers less than zero, and they have a minus sign in front of them. In our example, we encounter \(-3\) and \(-4\). When adding two negative numbers like \(-3\) and \(-4\), you get a more negative number, which is \(-7\). Subtracting a negative number is like adding a positive. For instance, \(2 - (-7)\) turns into \(2 + 7\). Remember these rules to handle negative numbers confidently.
Parentheses in Algebra
Parentheses in algebra denote that the operations inside them should be performed first. This rule is part of the order of operations (PEMDAS/BODMAS). In our given expression \(2 - (-3 + (-4))\), we first need to work inside the parentheses: \(-3 + (-4)\). This gives us \(-7\). So, the expression simplifies to \(2 - (-7)\). Ignoring parentheses or not simplifying them correctly will lead to errors. Always look out for parentheses and simplify what's inside them before moving on.

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