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Chapter 9: Problem 37

Find the value of each of the following expressions when \(x=4\). $$3 x-5$$

Short Answer

Expert verified
The expression evaluates to 7 when \(x=4\).

Step by step solution

01

Identify the expression and substitution value

We are given the expression \(3x - 5\) and need to evaluate it by substituting \(x = 4\). This involves replacing \(x\) in the expression with \(4\) to find the value of the expression.
02

Substitute the value of \(x\)

Substitute \(4\) for \(x\) in the expression, resulting in \(3(4) - 5\).
03

Perform multiplication

First, perform the multiplication in the expression. Calculate \(3 \times 4 = 12\).
04

Perform subtraction

Now subtract \(5\) from \(12\) to get the result: \(12 - 5 = 7\).

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Key Concepts

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

Understanding Substitution in Algebra
In algebra, substitution is a fundamental concept that allows us to solve expressions by replacing variables with given values. This approach simplifies expressions and is essential in evaluating mathematical expressions correctly. Let's break down the substitution process:
  • First, identify the variable in the expression that needs replacing. In our example, the expression is \(3x - 5\) and the variable is \(x\).
  • Next, substitute the given value for the variable. The problem states that \(x = 4\), so we replace every \(x\) in the expression with \(4\).
With substitution, you are effectively changing the algebraic expression into something numeric by replacing the letter (or variable) with a specific number. This facilitates the use of arithmetic operations to find the expression's value.
Exploring Basic Arithmetic Operations
Once you've substituted the variable with its respective value, the next step involves performing basic arithmetic operations. This is crucial for solving the expression completely. In our example, we must undertake a multiplication followed by a subtraction:
  • Multiplication: After substituting \(x = 4\) into the expression, it becomes \(3(4) - 5\). The first arithmetic operation to perform here is the multiplication \(3 \times 4\).
  • Subtraction: Once you've got the result of the multiplication, which is \(12\), the next step is to perform the subtraction: \(12 - 5\).
These operations follow the order of operations, which is vital in algebra, ensuring calculations are done in the correct sequence. Multiplication comes before subtraction, ensuring precision and accuracy in determining the final result.
Solving Prealgebra Problems
Prealgebra serves as a foundation for all algebraic concepts, underpinning everyday math skills. It primarily revolves around understanding the relationships between numbers and performing calculations. Evaluating expressions like \(3x - 5\) when \(x = 4\) is an example of a prealgebra problem. Here's why such exercises are important:
  • They reinforce the basics of operations such as addition, subtraction, multiplication, and division.
  • Pave the way for understanding more complex algebraic concepts by honing problem-solving skills.
  • Provide practice in substituting values and calculating their effect on expressions.
By mastering prealgebra, students develop confidence and competence to tackle more advanced algebraic concepts with ease, setting a strong mathematical foundation for future studies.

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Most popular questions from this chapter

Multiply the following expressions. \(\left(8 a^{4} b^{4}\right)\left(5 a^{3} b^{5}\right)\left(a^{2} b^{6}\right)\)

Expand and multiply. $$(6 x+7)^{2}$$

Multiply the following expressions. $$(6 x-1)(3 x+1)$$

Simplify the following expressions. \(\left(9 a^{5} b^{6}\right)^{2}\left(8 a^{5} b\right)\)

Expand and multiply. $$(4 x+1)^{2}$$
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