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Chapter 4: Problem 69

Evaluate \(5 x-3\) for each value. $$x=-1$$

Short Answer

Expert verified
The evaluated expression is -8

Step by step solution

01

Identify the Expression and the Value to be substituted

The algebraic expression given in this task is \(5x - 3\) and the value of \(x\) that needs to be substituted into this expression is -1.
02

Substitute the Value

Now plug the given value of \(x\) i.e., -1 into the expression. We obtain \(5(-1) - 3\) when -1 is substituted for \(x\).
03

Perform the Calculations

Next, perform the multiplication and subtraction given in the expression, that results in \(-5 - 3\). So, \(-5 - 3 = -8\).

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Key Concepts

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

Substitution
Substitution in algebra involves replacing a variable in an expression or equation with a specific numerical value. This is a fundamental skill in algebra, as it allows us to evaluate expressions and solve equations. Let's break down this concept:
  • Identify the variables in your algebraic expression.
  • Determine the specific values you will substitute in place of these variables.
  • Replace the variable(s) with the number(s) you've determined.
For example, in our expression, the variable is \( x \). We substitute \( x = -1 \) into the expression \( 5x - 3 \), giving us \( 5(-1) - 3 \). This process transforms the algebraic expression into a numerical one that we can easily calculate.
Evaluating Expressions
Once substitution is complete, the next step is evaluating the expression. Evaluating simply means finding the value of the expression after substitution. Here are the steps:
  • Perform any multiplication or division first. In \( 5 \times (-1) \), the multiplication yields \(-5\).
  • Next, proceed to addition or subtraction. With \(-5 - 3\), subtracting gives us \(-8\).

It's crucial to follow the order of operations. Remember: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Multiplication precedes subtraction, ensuring accurate evaluation of the expression. So, the evaluated expression \( 5x - 3 \) with \( x = -1 \) results in \(-8\).
Basic Algebra
Basic algebra is all about working with variables and numbers to solve problems. It includes concepts like substitution and evaluating expressions. Here's a simple overview:
  • Variables: Symbols, often letters, that represent numbers.
  • Algebraic Expressions: Combinations of variables, numbers, and operations (like \(+\), \(-\), \(\times\), and \(\div\)).
  • Simplification: Using algebraic rules to rewrite expressions in a simpler form, sometimes through substitution.
In our exercise, the expression \( 5x - 3 \) is simplified by substituting \( x = -1 \) and evaluated to a single number \(-8\). This process highlights the core principles of algebra: replacing variables, following operations, and calculating to find solutions. It's essential to practice these skills to solve more complex algebraic problems efficiently.

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Most popular questions from this chapter

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