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Chapter 3: Problem 463

In the following exercises, evaluate each expression. $$ 5 a+8 b \text { when } a=-2, b=-6 $$

Short Answer

Expert verified
-58

Step by step solution

01

Substitute the values of the variables

Replace the variable 'a' with -2 and 'b' with -6 in the expression. The expression becomes:\[ 5(-2) + 8(-6) \]
02

Multiply the coefficients with the substituted values

First, multiply 5 by -2 and then multiply 8 by -6:\[ 5(-2) = -10 \]\[ 8(-6) = -48 \]
03

Add the products from Step 2

Finally, add the results from the previous step:\[ -10 + (-48) = -10 - 48 = -58 \]

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Key Concepts

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

Substitution
Substitution is a fundamental concept in algebra. It involves replacing variables in an expression with the given values. To substitute correctly, always make sure to use parentheses around the values, especially when they are negative. This helps in maintaining the correct order of operations and avoiding common mistakes. For example, in the expression 5a + 8b when a = -2 and b = -6, replacing 'a' and 'b' gives: 5(-2) + 8(-6)
Multiplication
Multiplication is often the next step after substitution. In our example, we need to multiply the coefficients (numbers in front of the variables) by their substituted values:
  • 5 脳 (-2) = -10
  • 8 脳 (-6) = -48
Always multiply the numbers carefully and keep track of the signs. Remember that multiplying two negative numbers will give a positive result, but here, both numbers being multiplied with positive coefficients are negative, thus resulting in negative products.
Addition
After substitution and multiplication, the final step is addition. When adding numbers, be mindful of their signs. For instance, in our problem, after multiplying, we have -10 and -48. Adding these together involves recognizing that both numbers are negative:
  • -10 + (-48) can be rephrased as -10 - 48
  • This computation results in a more negative number, giving us -58
It鈥檚 helpful to think of adding negative numbers like moving further left on the number line.

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