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Chapter 5: Problem 87

Evaluate each expression for \(x=6, y=0.3,\) and \(z=-2.4 .\) $$ 4 y-z $$

Short Answer

Expert verified
The expression evaluates to 3.6.

Step by step solution

01

Substitute the values

Substitute the given values of the variables into the expression. The expression is \(4y - z\). With \(y = 0.3\) and \(z = -2.4\), the expression becomes \(4 \times 0.3 - (-2.4)\).
02

Simplify multiplication

Multiply 4 by 0.3 to find the first part of the expression: \(4 \times 0.3 = 1.2\).
03

Simplify subtraction

The expression now is \(1.2 - (-2.4)\). When subtracting a negative number, it becomes addition: \(1.2 + 2.4\).
04

Final simplification

Add 1.2 and 2.4 to get the final result: \(1.2 + 2.4 = 3.6\).

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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 first step in solving any algebraic expression. It's like a treasure hunt where you replace symbols with numbers. In our exercise, the expression given is \(4y - z\). The problem provides specific values for variables: \(y = 0.3\) and \(z = -2.4\).
Applying Variable Substitution:
  • Identify the variables in the expression. Here, they are \(y\) and \(z\).
  • Substitute the corresponding values for each variable in the expression.
This will transform the algebraic expression into a numerical expression. After substitution, our expression becomes \(4 \times 0.3 - (-2.4)\).
Each variable is like a placeholder, and by substituting, you personalize the expression. This step is essential to move forward to the next stages of solving the problem.
Expression Evaluation
Once you've substituted all the variables, the next step is evaluating the expression. This step involves performing the arithmetic operations as indicated in the expression.
Breaking Down the Evaluation Process:
  • Start with any multiplication or division as these come first in the order of operations (often remembered by "PEMDAS" - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
  • In our example, the expression is now \(4 \times 0.3 - (-2.4)\).
  • Perform the multiplication: \(4 \times 0.3 = 1.2\).
  • Next, handle the subtraction of a negative number: \(1.2 - (-2.4)\). Subtracting a negative is the same as adding: \(1.2 + 2.4\).
Thus, the expression evaluation is taking us closer to the solution by ensuring all operations are carried out correctly according to their respective priorities.
Simplifying Expressions
The final task is simplifying the expression to reach the answer. Simplification involves combining like terms and reducing the expression to its simplest form. In our case, after handling the operations, we're left with \(1.2 + 2.4\).
The Simplification Process:
  • After carrying out the arithmetic operations, combine the numbers or terms.
  • Add the numbers: \(1.2 + 2.4 = 3.6\).
  • Ensure no further simplifications are possible and double-check your calculations.
Simplification gives you the neat, final form of the expression, making it both efficient and elegant. It's the last step where all previous work comes together for the final solution. In many math problems, this is what gives you your complete answer, which in this case, is 3.6.

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Most popular questions from this chapter

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