Problem 311 Evaluate each expression. \(2 ... [FREE SOLUTION]

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Chapter 1: Problem 311

Evaluate each expression. \(2 w^{2}-3 w+7\) when \(w=-2\)

Short Answer

Expert verified

Step by step solution

- Substitute the value of w

Replace the variable w in the expression with -2. The expression becomes \(2(-2)^{2}-3(-2)+7\).

- Evaluate the exponent

Calculate the square of -2. \((-2)^{2} = 4\). The expression now is \(2(4)-3(-2)+7\).

- Multiply

Multiply 2 by 4 and -3 by -2. \(2(4) = 8\) and \(-3(-2) = 6\). Now the expression is \(8+6+7\).

- Add the results

Add 8, 6, and 7 together. \(8 + 6 + 7 = 21\).

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Key Concepts

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

Substitution

Substitution is the process of replacing a variable with a specific value. In our example, we have the expression \(2 w^{2}-3 w+7\) and we need to evaluate it when \(w=-2\). To do this, we substitute -2 wherever we see the variable \(w\) in the expression.
So, our expression becomes \(2(-2)^{2}-3(-2)+7\).
Substitution is helpful because it allows us to simplify and solve expressions that have variables by giving us specific numbers to work with.

Exponents

Exponents tell us how many times to multiply a number by itself. In our example, we encounter the term \((-2)^{2}\). This means we need to multiply -2 by itself:

First multiplication: -2 \(\times\) -2 = 4

This change simplifies our expression further. So, \(2(-2)^{2}-3(-2)+7\) becomes \(2(4)-3(-2)+7\).
Understanding exponents is essential because they frequently appear in algebraic expressions, and properly evaluating them is a crucial step in solving these problems.

Multiplication

Multiplication involves calculating the product of two numbers. In our simplified expression, we have \(2(4)\) and \(-3(-2)\) to evaluate. Here鈥檚 how we do it:

\(2 \times 4 = 8\)
-3 \(\times\) -2 = 6 (multiplying two negative numbers results in a positive number)

So now, our expression becomes \(8 + 6 + 7\).
By clearly performing each multiplication step-by-step, we ensure accuracy and make the process easier to understand.

Addition

Addition combines values to find the sum. At this point, our expression is \(8 + 6 + 7\). We add these values together one step at a time:

Adding 8 and 6 equals 14: \(8 + 6 = 14\)
Now, we add 14 and 7: \(14 + 7 = 21\)

Thus, the final evaluated expression is 21.
Practicing addition with simple numbers strengthens your basic math skills and builds confidence in managing more complex expressions in algebra.

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91影视

Evaluate each expression. \(2 w^{2}-3 w+7\) when \(w=-2\)

Short Answer

Step by step solution

- Substitute the value of w

- Evaluate the exponent

- Multiply

- Add the results

Key Concepts

Substitution

Exponents

Multiplication

Addition

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