Problem 61 Evaluate each expression if \(a=... [FREE SOLUTION]

Chapter 2: Problem 61

Evaluate each expression if $a=6, b=10,$ and $c=3$ $$2 b-6$$

Short Answer

Expert verified

The expression evaluates to 14.

Step by step solution

Substitute the Given Values

Substitute the value of the variable $b$ into the expression. Since $b = 10$, the expression becomes $2 \times 10 - 6$.

Perform the Multiplication

Multiply the constant 2 by the value substituted for $b$. So, $2 \times 10 = 20$.

Complete the Subtraction

Subtract 6 from the result of the multiplication. Therefore, $20 - 6 = 14$.

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Key Concepts

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

Evaluation of Expressions

Evaluating algebraic expressions involves finding the numeric value of an expression for given values of variables. Think of it as asking, "What number do I get if I plug these numbers in?" For example, in the expression $2b - 6$, you can replace the variable $b$ with its given value, which is 10. The expression becomes $2 \times 10 - 6$. The goal is to simplify this expression into a single numerical value, following arithmetic operations. This process helps us understand how changes in variable values affect the overall result of the expression.

Substitution in Algebra

Substitution is like solving a puzzle where each letter (variable) is given a specific number to take its place. When you're asked to substitute in algebra, you replace each variable with the number it represents. For instance, given $b = 10$, you substitute 10 in place of $b$ in the expression $2b - 6$. So, it turns into $2 \times 10 - 6$. This step ensures that the variables are replaced consistently so the math operations can be carried out smoothly. Substitution helps simplify the problem and makes it easier to reach the final answer.

Order of Operations

Order of operations is a set of rules that determine the sequence in which calculations should be performed to ensure consistent results. You've probably heard of PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).When evaluating expressions like $2 \times 10 - 6$, start with multiplication before moving on to subtraction. Follow these steps to ensure you're doing it correctly:

Perform any operations inside parentheses first.
Calculate exponents.
Then, handle multiplication or division from left to right.
Finally, do addition and subtraction from left to right.

In this case, multiplication ($2 \times 10$) is performed before subtraction, giving us the final result of 14.

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91影视

Evaluate each expression if \(a=6, b=10,\) and \(c=3\) $$2 b-6$$

Short Answer

Step by step solution

Substitute the Given Values

Perform the Multiplication

Complete the Subtraction

Key Concepts

Evaluation of Expressions

Substitution in Algebra

Order of Operations

One App. One Place for Learning.

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