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Chapter 1: Problem 34

Evaluate each expression using the values provided. $$ 5+(2 x-3), \text { for } x=8 $$

Short Answer

Expert verified
18

Step by step solution

01

Substitute the Value of x

Substitute the given value of x into the expression. The expression is \(5 + (2x - 3)\), and x is given as 8. So, substitute 8 for x: \(5 + (2(8) - 3)\).
02

Simplify Inside the Parentheses

First, perform the multiplication inside the parentheses. Compute \(2 \times 8\): \(5 + (16 - 3)\).
03

Finish Simplifying the Parentheses

Now, perform the subtraction inside the parentheses: \(5 + 13\).
04

Compute the Final Answer

Finally, add the remaining numbers: \(5 + 13 = 18\).

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Key Concepts

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

Substitution
Substitution is the process of replacing a variable with its given value. In this problem, we have the expression \(5 + (2x - 3)\) and the value of \( x \) is provided as 8. To begin, substitute 8 for \( x \). This means replacing every instance of \( x \) in the expression with 8. Our expression now looks like this: \(5 + (2(8) - 3)\).
Simplifying Expressions
Simplifying expressions involves performing arithmetic operations within the brackets and combining like terms to reduce the expression to its simplest form. Look at \(5 + (2(8) - 3)\). First, handle the multiplication inside the parentheses. Compute \(2 \times 8\), which equals 16. Now, the expression becomes \(5 + (16 - 3)\). Next, perform the subtraction within the parentheses: \(16 - 3\), resulting in 13. So, we get \(5 + 13\).
Order of Operations
The Order of Operations is a set of rules used to determine the sequence in which calculations are performed. The common rule to remember is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Following these rules ensures that we evaluate expressions correctly. In the expression \(5 + (2(8) - 3)\), we handle the parentheses first, then the multiplication, followed by the subtraction, and finally the addition. This rule helped us reduce the expression step-by-step to obtain the final result.
Arithmetic Operations
Understanding basic arithmetic operations is crucial when working with expressions. These operations include addition, subtraction, multiplication, and division. In our example, the expression \(5 + (2(8) - 3)\) requires you to perform multiplication first: \(2 \times 8 = 16\). Then, subtraction: \(16 - 3 = 13\). Finally, addition: \(5 + 13\), which gives us 18. Mastering these operations is essential for evaluating and simplifying expressions accurately.

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