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Magazine Chapter 2: Problem 3
Evaluate each expression if \(x=6\). a. \(2 x+3\) b. \(2(x+3)\) c. \(5 x-13\) d. \(\frac{x+9}{3}\)
Short Answer
Expert verified
a. 15, b. 18, c. 17, d. 5.
Step by step solution
01
Substitute in Expression a
First, evaluate the expression \(2x + 3\) where \(x = 6\). Substitute \(x\) with 6: \[ 2(6) + 3 \]
02
Calculate Expression a
Perform the multiplication and addition: \[ 2 \times 6 + 3 = 12 + 3 = 15 \]Therefore, the value of the expression for part (a) is 15.
03
Substitute in Expression b
Evaluate the expression \(2(x + 3)\) where \(x = 6\). Substitute \(x\) with 6: \[ 2(6 + 3) \]
04
Calculate Expression b
First, perform the operation inside the parentheses, then multiply: \[ 2(6 + 3) = 2(9) = 18 \]The value of the expression for part (b) is 18.
05
Substitute in Expression c
Evaluate the expression \(5x - 13\) where \(x = 6\). Substitute \(x\) with 6: \[ 5(6) - 13 \]
06
Calculate Expression c
Perform the multiplication and subtraction: \[ 5 \times 6 - 13 = 30 - 13 = 17 \]The value of the expression for part (c) is 17.
07
Substitute in Expression d
Evaluate the expression \(\frac{x + 9}{3}\) where \(x = 6\). Substitute \(x\) with 6: \[ \frac{6 + 9}{3} \]
08
Calculate Expression d
First, perform the addition in the numerator, then divide: \[ \frac{6 + 9}{3} = \frac{15}{3} = 5 \]The value of the expression for part (d) is 5.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Substitution Method
The substitution method in algebra involves replacing a variable with a given number or another expression. This is necessary when a specific value for the variable is provided, such as when we have to evaluate expressions like the ones in the exercise. Here, we are given that \(x = 6\).
- Start by taking each expression and substituting \(x\) with the number 6.
- With the original expressions, replace every occurrence of the variable with the given number.
- This converts algebraic expressions into numerical ones that are easier to solve.
Evaluating Expressions
Once substitution is done, evaluating expressions becomes a sequence of simple arithmetic calculations. To evaluate means to calculate the value of an expression by performing all the indicated operations. For example, consider the expression \(2x + 3\) when \(x = 6\):
- After substitution, the expression becomes \(2(6) + 3\).
- Calculate it step-by-step as you would follow the PEMDAS/BODMAS rule.
- Perform multiplication first, and then addition.
Basic Arithmetic Operations
Basic arithmetic operations form the foundation for evaluating algebraic expressions. They include addition, subtraction, multiplication, and division. Understanding and correctly applying these operations will enable you to simplify and solve expressions after substitution. Let's break down how to handle these operations:
- **Multiplication and Division:** Perform these operations before addition and subtraction, as per the order of operations rules.
- **Addition and Subtraction:** After multiplying and dividing, move on to addition or subtraction , and tackle them from left to right.
- **Working with Parentheses:** Always resolve expressions inside parentheses first, and apply multiplication afterwards if needed.
