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Chapter 5: Problem 85

Evaluate each expression for \(x=6, y=0.3,\) and \(z=-2.4 .\) $$ x-y $$

Short Answer

Expert verified
The result is 5.7.

Step by step solution

01

Understand the Expression

The expression we need to evaluate is \(x - y\), where \(x = 6\) and \(y = 0.3\). We'll substitute these values into the expression.
02

Substitute Values

Plug in the given values into the expression \(x - y\). So it becomes \(6 - 0.3\).
03

Perform Subtraction

Calculate the result of the subtraction: \(6 - 0.3 = 5.7\).
04

Verify Solution

Double-check the calculation to ensure accuracy. Since \(6\) and \(0.3\) are both accurate to one decimal place, the subtraction \(6 - 0.3\) should indeed equal \(5.7\).

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Key Concepts

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

Substitution in Algebra
Substitution in algebra involves replacing variables in an expression with specified numerical values. This step simplifies the abstract problem, converting it into a straightforward arithmetic problem. To perform substitution, identify the variables and their corresponding values in the expression. For instance:
  • In the expression \(x - y\), if \(x = 6\) and \(y = 0.3\), substitute the variables with these numbers.
  • It transforms the expression from \(x - y\) to \(6 - 0.3\).
By substituting correctly, the complexity is reduced, and you prepare the expression for calculation. Substitution helps in focusing purely on arithmetic operations, allowing for systematic problem-solving.
Arithmetic Operations
Arithmetic operations are fundamental mathematical procedures that involve addition, subtraction, multiplication, and division. These operations help solve expressions after substitution. In this exercise, the key operation is subtraction:
  • Once values are substituted, perform the arithmetic operation directly on these numerical values.
  • For example, the simplified expression \(6 - 0.3\) is solved by subtracting 0.3 from 6.
The result of this calculation is \(5.7\), reflecting the importance of accurately executing arithmetic operations. Using clear mental subtraction or paper can help ensure steps are precise and consistent.
Checking Calculations
Checking your calculations is a crucial step to avoid errors and ensure the accuracy of your results. Even simple arithmetic calculations can sometimes result in mistakes; hence, it is vital to verify:
  • Review each step of your arithmetic operation. Go over your subtraction in \(6 - 0.3\) and ensure each decimal placement is correct.
  • Re-calculate manually or using a calculator to cross-check this arithmetic operation, confirming the result \(5.7\).
Reassurance through checking solidifies your understanding of mathematical procedures and boosts confidence in problem-solving. Consistent accuracy checking becomes a beneficial habit in more complex arithmetic and algebraic expressions.

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