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Chapter 2: Problem 15

Evaluate. \(34 a\), where \(a=32\)

Short Answer

Expert verified
The evaluated expression is 1088.

Step by step solution

01

Substitute the value of 'a'

Replace the variable \(a\) in the expression \(34a\) with the given value \(32\). This gives us \(34 \times 32\).
02

Multiply the constants

Now, multiply the constants \(34\) and \(32\). Perform the multiplication: \(34 \times 32 = 1088\).

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Key Concepts

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

Substitution
Substitution is an essential concept in algebra that helps us simplify expressions and solve equations. It involves replacing a variable within an expression or equation with a specific value given. This process is crucial because it transforms abstract expressions into more concrete numbers, making them easier to work with.

In the example exercise, we needed to evaluate the expression \(34a\) with a given \(a = 32\). By substituting in this case, we replaced the variable \(a\) with the number 32. Thus, the expression \(34a\) became \(34 \times 32\). By converting our expression into something completely numerical, it allows us to proceed to the next steps with ease.
Multiplication of Constants
Multiplication of constants is a straightforward mathematical operation. It involves taking two values and calculating their product. When given constants, it simply means multiplying non-variable numbers together.

Once substitution has occurred in an algebraic expression, such as turning \(34a\) into \(34 \times 32\), we engage in multiplying constants. In this step, we multiply the numbers 34 and 32. Doing the math, we find that \(34 \times 32 = 1088\).

Here's why understanding multiplication of constants is important:
  • It strengthens your foundational abilities in arithmetic.
  • Allows for calculation of values quickly and without error.
  • Applies directly when handling arithmetic operations in algebraic expressions.
When you master this skill, it becomes much easier to handle complex problems.
Evaluating Expressions
Evaluating expressions refers to finding the numeric value of an expression after processes like substitution and simplification have been applied. It's the final step, where you derive a specific result.

To evaluate an algebraic expression means to perform all the required mathematical operations in order to find its simplest form. In our example, we substituted the value of \(a\) into the expression, leading to \(34 \times 32\). Then, through multiplication, the evaluation yielded the result 1088.

A few key considerations when evaluating:
  • Ensure that all substitutions are correct before proceeding.
  • Keep operations organized to avoid mistakes.
  • Always double-check your answers for consistency.
By carefully following these steps, you can reliably evaluate expressions and confirm their correctness.

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Most popular questions from this chapter

Determine the inequality given the answers expressed in interval notation. $$ (-\infty, 3) $$

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ 12 x-2<-1 \text { or } 12 x-2>1 $$

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ -3 x+1<-5 \text { or }-4 x-3>-23 $$

The sum of three consecutive odd integers is \(45 .\) Find the integers.

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ -5<2(x-1)-3(x+2)<5 $$
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