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Chapter 2: Problem 80

In the following exercises, evaluate the expression for the given value. $$x^{2}+5 x-8 \text { when } x=6$$

Short Answer

Expert verified
58

Step by step solution

01

- Substitute the given value

First, substitute the given value of x into the expression. The expression is \(x^2 + 5x - 8\), and the given value is \(x = 6\). Therefore, substitute 6 for x: \(6^2 + 5(6) - 8\).
02

- Calculate the square term

Calculate the value of \(6^2\). We get \(6^2 = 36\), so the expression becomes \(36 + 5(6) - 8\).
03

- Multiply the coefficients

Next, multiply 5 by 6 to get \(5(6) = 30\). Now our expression is \(36 + 30 - 8\).
04

- Perform the addition

Add 36 and 30 together. This gives us \(36 + 30 = 66\), so the expression simplifies to \(66 - 8\).
05

- Perform the subtraction

Finally, subtract 8 from 66. This gives us \(66 - 8 = 58\). So the value of the expression when \(x = 6\) is 58.

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Key Concepts

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

Substitution in Algebra
Substitution in algebra is an essential concept. It involves replacing a variable with a given number to evaluate an expression. To understand this better, consider the expression given in the exercise: \( x^2 + 5x - 8 \). Here, we are asked to evaluate the expression when \( x = 6 \).
First, substitute 6 for every occurrence of \( x \) in the expression. This means we replace \( x \) with 6, transforming the expression into \( 6^2 + 5(6) - 8 \).

Performing substitution accurately is critical. Misplacing or forgetting to substitute all instances of a variable can lead to wrong answers. Remember to take your time and check each variable in the expression.
Simplifying Expressions
Simplifying expressions is about making a math problem easier to handle by combining like terms and performing basic operations. Once substitution is done, as in our example \( 6^2 + 5(6) - 8 \), the next step is simplifying.
Let's simplify step by step:
  • First, calculate the square term: \( 6^2 \). This equals 36. So, the expression now is \( 36 + 5(6) - 8 \).
  • Next, perform the multiplication: \( 5 \times 6 \). This equals 30. Now, our expression is \( 36 + 30 - 8 \).
  • Then, combine the addition terms: \( 36 + 30 \). This equals 66. Now, the simplified expression is \( 66 - 8 \).
  • Finally, perform the subtraction: \( 66 - 8 \). This equals 58.

Simplification helps you break down complex expressions. Be patient with each step and verify your work. Double-check each transformation to ensure accuracy.
Order of Operations
Order of operations is a set of rules to determine the correct order in which to solve parts of an expression. An easy way to remember these rules is the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (i.e., powers and roots)
  • M/D: Multiplication and Division (left to right)
  • A/S: Addition and Subtraction (left to right)
Applying this to our example, \( 6^2 + 5(6) - 8 \):
  • First, we dealt with the exponent: \( 6^2 = 36 \).
  • Then, we performed the multiplication: \( 5(6) = 30 \).
  • Followed by the addition: \( 36 + 30 = 66 \).
  • Lastly, we did the subtraction: \( 66 - 8 = 58 \).

The order of operations is critical to get the correct result in a structured manner. It ensures every mathematical expression is solved accurately and consistently.

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Most popular questions from this chapter

In the following exercises, solve each equation using the addition property of equality. $$ y-3=19 $$

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In the following exercises, evaluate each expression. Simplify by combining like terms. A. \(6 x+8 x\) B. \(6 x+8 x\)

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