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Chapter 1: Problem 93

\(-x+y-z\) for \(x=3, y=-4\), and \(z=-6\)

Short Answer

Expert verified
The result is -1.

Step by step solution

01

Substitute the given values into the expression

We have the expression \(-x + y - z\). Given that \(x = 3\), \(y = -4\), and \(z = -6\), we substitute these values into the expression. Thus, the expression becomes \(-3 + (-4) - (-6)\).
02

Simplify the expression by calculating each term

Start by simplifying the expression step by step: 1. \(-3\) stays as it is since it is the first term.2. \(+ (-4)\), which is equivalent to \(-4\).3. \(- (-6)\), which is equivalent to \(+ 6\) because subtracting a negative is like adding a positive.
03

Perform the arithmetic operations

With the simplified expression \(-3 - 4 + 6\), perform the operations from left to right:1. Calculate \(-3 - 4\) which equals \(-7\).2. Then calculate \(-7 + 6\) which equals \(-1\). This gives the final result of the expression.

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Key Concepts

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

Substitution
Substitution is an essential step in solving algebraic expressions. It involves replacing variables in an expression with known values. In our exercise, we have the algebraic expression \(-x + y - z\).
First, determine the values for each variable: in this case, \(x = 3\), \(y = -4\), and \(z = -6\).
  • Replace each instance of the variable in the expression: replace \(x\) with \(3\), \(y\) with \(-4\), and \(z\) with \(-6\).
  • Now, the expression becomes \(-3 + (-4) - (-6)\).
Substitution allows us to convert abstract algebraic expressions into numerical expressions, which can be easily computed.
Simplification
Simplification in algebra means transforming a complex expression into a simpler and more easily evaluable form. After substitution, our expression was \(-3 + (-4) - (-6)\).
At this point, we simplify by rewriting terms and resolving operations:
  • Start with \(-3\) which remains unchanged since it's the first term.
  • Next, resolve \(+ (-4)\) to just \(-4\) since adding a negative is the same as subtracting.
  • For \(- (-6)\), recognize that subtracting a negative transforms it into a positive, so it becomes \(+6\).
This gives us the simplified expression \(-3 - 4 + 6\). Simplification is vital as it makes expressions easier and less cumbersome to solve.
Integer Operations
Once we have a simplified expression, it becomes straightforward to perform integer operations. Now, with the simplified expression \(-3 - 4 + 6\), we focus on performing arithmetic operations in sequence:
  • Start with \(-3 - 4\): Subtracting these integers gives us \(-7\).
  • Then, take \(-7 + 6\): Adding \(+6\) to \(-7\) results in \(-1\).
Understanding integer operations is key for solving algebraic expressions. This sequence of operations might be simple, but it highlights the importance of following order in arithmetic tasks. It ensures accurate results and builds a fundamental understanding of how arithmetic works within mathematical expressions.

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Most popular questions from this chapter

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$-46(-73-27)$$

Simplify each algebraic expression by combining similar terms. $$-2(m+3)-3(m-1)+8(m+4)$$

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$17+(-18)-19-14+13-17$$

Simplify each algebraic expression by combining similar terms. $$-9 y+5 y-7 y$$

State whether the expressions in each problem are equivalent and explain why or why not. \((-6 a+7 b)+11 c\) and \(7 b+(11 c-6 a)\)
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