Problem 3 Evaluate each expression for \(x... [FREE SOLUTION]

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Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 3

Evaluate each expression for $x=4$. $$12-x$$

Short Answer

Expert verified

The substitution of x = 4 in the expression $12 - x$ results in 8.

Step by step solution

Understand the expression

The given algebraic expression is $12 - x$. Here $x$ is the variable.

Substitute the given value of variable

We need to substitute $x$ (which is 4 in this case) into this expression. After substitution, the equation will be $12 - 4$.

Simplify the expression

After the substitution, simplify the numeric expression resulting into 8.

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Key Concepts

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

Algebraic Expression

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In the expression $12 - x$, we see the combination of a number (12), a variable $x$, and a subtraction operation. Here, an unknown or variable $x$ represents a number that can change based on the given situation or requirement.
An algebraic expression does not have an equality sign. It's different from an equation, which shows two sides that are equal. Expressions can be simplified but not solved unless they become equations with specified values for the variables.

Variable Substitution

Variable substitution is an essential step in evaluating expressions. It involves replacing the variable in an expression with a given numerical value. In the context of the exercise, the expression $12 - x$ required us to substitute $x$ with 4.
To correctly substitute:

Identify the variable in the expression.
Replace the variable with the provided value (in this case, $x = 4$) in all instances where it appears in the expression.

After performing the substitution, the algebraic expression becomes a numeric one. This step allows us to move forward and find a definitive answer.

Numeric Simplification

Numeric simplification is often the final step in solving algebraic expressions after substitution. In our example, after replacing $x$ with 4, the new expression was $12 - 4$.
To simplify this:

Perform the arithmetic operation indicated.
Here, subtract 4 from 12 to get 8.

Simplification involves reducing the numeric expression to its smallest possible value. It's important not only for finding answers but also for preparing more complex expressions for further operations or comparisons. Simplifying ensures clarity and helps in checking the correctness of earlier steps.

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91影视

Evaluate each expression for \(x=4\). $$12-x$$

Short Answer

Step by step solution

Understand the expression

Substitute the given value of variable

Simplify the expression

Key Concepts

Algebraic Expression

Variable Substitution

Numeric Simplification

One App. One Place for Learning.

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