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Chapter 2: Problem 448

In the following exercises, evaluate each expression. $$ 6 a-2 b \text { when } a=5, b=7 $$

Short Answer

Expert verified
The expression evaluates to 16.

Step by step solution

01

Identify the given values

Assign the values of the variables given in the problem. Here, we have \(a = 5\) and \(b = 7\).
02

Substitute the values into the expression

Replace the variables \(a\) and \(b\) in the expression \(6a - 2b\) with the given values: \[6(5) - 2(7)\].
03

Multiply the constants

Perform the multiplications: \(6 \times 5 = 30\) and \(2 \times 7 = 14\). So the expression now becomes: \[30 - 14\].
04

Perform the subtraction

Subtract the results of the multiplications: \[30 - 14 = 16\].

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Key Concepts

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

Substitution in Algebra
In algebra, substitution is a method where we replace variables with their corresponding values to simplify the expressions. Think of it like replacing placeholders with actual numbers to find out what the expression equals.
For example, in the given problem, we need to evaluate the expression [6a - 2b] where a = 5 and b = 7.
We start by substituting the values into the expression. This means we replace 'a' with 5 and 'b' with 7, resulting in:
[6(5) - 2(7)].
This substitution helps break down the problem into more manageable parts.

Multiplication in Algebra
Multiplication in algebra often involves multiplying constants with variables or numbers derived from variables.
Once we have substituted the values into our expression, the next step is to multiply these constants.
From the expression [6(5) - 2(7)], we perform the multiplications:
  • 6 times 5 which gives us 30
  • 2 times 7 which gives us 14

Multiplying first makes sure that we are following the right steps to simplify the expression. These intermediate results will be used in subsequent steps to get the final answer.

Order of Operations
Order of operations is a fundamental principle in mathematics that dictates the sequence in which we perform different operations within an expression. This ensures everyone follows the same process to arrive at the correct answer.
The order is often remembered by the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division
  • Addition and Subtraction

In our case, we focus on multiplication and subtraction. After substituting and multiplying, our simplified expression is [30 - 14].
The final step following the order of operations is to perform the subtraction:
[30 - 14 = 16].
This approach ensures clarity and accuracy, leading us to the correct evaluation of the given expression.

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