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Chapter 2: Problem 66

Evaluate each expression if \(a=-2, b=-6,\) and \(c=14\). $$c-a+b$$

Short Answer

Expert verified
The value of the expression is 10.

Step by step solution

01

Substitute the values for the variables

Replace each variable in the expression with the given values. The expression is \(c-a+b\). Substitute \(a = -2\), \(b = -6\), and \(c = 14\), resulting in \(14 - (-2) + (-6)\).
02

Simplify the expression

Simplify the expression by performing the operations. Start with \(14 - (-2)\), which simplifies to \(14 + 2\), giving \(16\).
03

Add the remaining values

Now add the result from the previous step to \(-6\): \(16 - 6 = 10\).

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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 step in evaluating algebraic expressions. It involves replacing variables with their given numerical values. When you see an exercise like evaluating the expression \(c-a+b\), it's essential to substitute the specified values for each variable. For instance, if \(a = -2\), \(b = -6\), and \(c = 14\), you will plug these numbers directly into the expression. This transforms \(c-a+b\) into \(14 - (-2) + (-6)\). Breaking down the abstract components into specific numbers makes the next steps of solving much clearer and easier to follow.
Simplification
Once substitution is complete, the next step is simplification. Simplification involves performing arithmetic operations to reduce the expression to its simplest form. From the earlier substitution example, you have the expression \(14 - (-2) + (-6)\). Simplify this step-by-step to make it more manageable:
  • First, handle any negative signs. Remember that subtracting a negative is equivalent to adding a positive.
  • Therefore, \(14 - (-2)\) becomes \(14 + 2\).
This results in \(16\). Always take care with signs, as they can make a significant difference in the final answer.
Integer Operations
Integer operations are at the core of evaluating expressions involving numbers. They include addition, subtraction, multiplication, and division of whole numbers. Continuing from the simplification part, you end with \(16 + (-6)\). With integer operations, you need to understand how to efficiently work with negative and positive numbers.
  • Adding a negative number is the same as subtracting the positive equivalent. Thus, \(16 + (-6)\) simplifies to \(16 - 6\).
  • When you carry out the subtraction, you end up with \(10\).
Remember, mastering integer operations is crucial as they form the basics of more advanced math concepts.

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