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Chapter 1: Problem 65

Evaluate. $$ 9-4 x, \text { for } x=5 $$

Short Answer

Expert verified
-11

Step by step solution

01

Substitute the value of x

Replace the variable x with 5 in the expression. The given expression is: \[9 - 4x\]. Substitute x = 5: \[9 - 4(5)\].
02

Perform multiplication

Multiply 4 by 5: \[9 - 20\].
03

Simplify the expression

Subtract 20 from 9 to get the final result: \[9 - 20 = -11\].

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Key Concepts

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

substitution method
The substitution method lets you evaluate an expression by replacing variables with their given values.
This means plugging in the provided numbers where the variables are.
In our exercise, we start by substituting the value of x with 5 in the expression 9 - 4x. The expression becomes 9 - 4(5).
Why is this important? It simplifies the process and eliminates unknowns.
Remember to correctly substitute each variable with its respective value before proceeding with any arithmetic operations.
evaluating expressions
Once you've substituted the variable, the next step involves evaluating the expression.
This means performing the arithmetic calculations indicated in the problem.
In this case, we transform the expression 9 - 4(5) by first performing the multiplication. Multiplication and division take precedence over addition and subtraction.
So, we multiply 4 by 5 to yield 20, simplifying our expression to 9 - 20.
This step is all about following the correct order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
simplification in algebra
Simplification is the final crucial step in solving algebra problems.
It involves reducing the expression to its simplest form.
Here, after substituting and evaluating the expression 9 - 4(5) to get 9 - 20, we simplify further. Subtraction is the final operation, so we subtract 20 from 9.
This results in our final answer: -11. Simplification helps verify that our solution is correct and makes it easier to understand.
Always check your work by simplifying to ensure all substitutions and calculations were performed accurately.

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