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Chapter 1: Problem 314

Evaluate each expression. \(7 m-4 n-2\) when \(m=-4\) and \(n=-9\)

Short Answer

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Step by step solution

01

Understand the Expression

The given expression is \(7m - 4n - 2\). Identify the values provided for the variables: \(m = -4\) and \(n = -9\).
02

Substitute the Values

Replace \(m\) and \(n\) in the expression with their given values. This gives:\(7(-4) - 4(-9) - 2\).
03

Multiply the Coefficients

Perform the multiplication:\(7(-4) = -28\) and \(-4(-9) = 36\). Substituting these results into the expression gives:\(-28 + 36 - 2\).
04

Simplify the Expression

Combine the terms step-by-step:First, add -28 and 36: \(-28 + 36 = 8\).Next, subtract 2 from the result:\(8 - 2 = 6\).

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Key Concepts

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

Substitution in Algebra
When we talk about substitution in algebra, we mean replacing variables in an expression with their given values. This is one of the first steps in evaluating an expression. Let's use our given expression as an example:

Suppose we have the expression:
  • 7m - 4n - 2
We are provided with the values for the variables, where m = -4 and n = -9. To solve, we substitute these values into our expression:
  • 7(-4) - 4(-9) - 2

It's crucial that you replace every instance of m with -4 and every instance of n with -9. Once you've done that, you're ready to move on to the next steps.
Multiplying Coefficients
In algebra, coefficients are the numerical parts of terms, and they need to be multiplied correctly. After substitution, our expression was 7(-4) - 4(-9) - 2. Let's break this down:
  • First, multiply 7 by -4:
    • 7(-4) = -28

  • Second, multiply -4 by -9:
    • -4(-9) = 36
These products then replace their corresponding terms in the original expression, giving us:
  • -28 + 36 - 2

Now we have simplified our expression to a point where the terms can be easily combined.
Simplifying Algebraic Expressions
Simplifying an algebraic expression involves combining like terms to reduce the expression to its simplest form. In our example, after performing the multiplications, we got:
  • -28 + 36 - 2
Combine these step-by-step:
  • First, combine -28 and 36:
    • -28 + 36 = 8

  • Second, subtract 2 from the result:
    • 8 - 2 = 6
The simplified value of the expression is 6.
Simplifying ensures that we understand and correctly solve the initial problem. It stresses the importance of following order of operations and handling negative signs accurately.

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