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Chapter 1: Problem 10

Find the value for \((a) x=4\) and \((b) x=6\). \(x-3\)

Short Answer

Expert verified
For \(x=4\), the value is 1. For \(x=6\), the value is 3.

Step by step solution

01

Understand the Expression

The given expression is \(x-3\). This expression tells us to subtract 3 from the value of \(x\).
02

Substitute and Solve for \(x=4\)

To find the value when \(x=4\), replace \(x\) with 4 in the expression: \(4-3\). Then perform the subtraction: \(4-3=1\).
03

Substitute and Solve for \(x=6\)

To find the value when \(x=6\), replace \(x\) with 6 in the expression: \(6-3\). Then perform the subtraction: \(6-3=3\).

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Key Concepts

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

substitution
First, let's talk about substitution. When we substitute, we replace a variable in an algebraic expression with a specific value. In algebra, variables are symbols like x, y, or z that stand for unknown numbers. Substitution is a way to see what happens when these symbols are replaced with actual numbers.
In our exercise, the expression is \(x - 3\). To substitute \(x\), we just need to plug in the given value of x into the expression. For example, if \(x = 4\), replace x with 4 and then simplify.
So, \(x-3\) becomes \(4-3\). Doing the subtraction gives us the final result.
evaluation
Next, let's discuss evaluation. Evaluation means finding the value of an algebraic expression after substituting the variables with their given values.
We only need to follow a few steps:
  • Substitute the value of the variable into the expression.
  • Perform the mathematical operations to simplify the expression.
For instance, in the given problem, once we substitute \(x = 4\), our expression \(x-3\) becomes \(4-3\). We then perform the subtraction to get the result, which is 1.
Similarly, if we substitute \(x = 6\), the expression becomes \(6-3\), and simplifying this gives us 3.
Evaluation helps us determine the outcomes of expressions for different values.
basic operations
Finally, let's review basic operations in algebra. These are the addition, subtraction, multiplication, and division that we perform to simplify expressions and solve equations.
In our example, the primary operation involved is subtraction. Subtraction means taking away one number from another. When we see the expression \(x-3\), it tells us to subtract 3 from the value of x.
Here鈥檚 a quick example:
  • When \(x = 4\), performing the subtraction \(4-3=1\).
  • When \(x = 6\), performing the subtraction \(6-3=3\).
Understanding how to perform these basic operations correctly is crucial for solving more complex algebraic expressions and equations effectively.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. Three-fourths of the sum of \(-8\) and 12

Among entertainment expenditures, the average annual spending per U.S. household on fees and admissions was \(\$ 526\) in 2001 . This amount decreased \(\$ 32\) by 2003 and then increased \(\$ 112\) by \(2006 .\) What was the average household expenditure for fees and admissions in \(2006 ?\)

Write a numerical expression for each phrase and simplify. The product of 4 and \(-7,\) added to \(-12\)

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Simplify each expression. $$ 8.4(6 t-6)+2.4(9-3 t) $$
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