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Chapter 2: Problem 52

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 5-x+2 $$

Short Answer

Expert verified
The simplified expression is \( 7 - x \)

Step by step solution

01

Identify Like Terms

Like terms are the terms having the same algebraic parts. These could be similar variables or constants. In this case, '5' and '2' are like terms.
02

Combine Like Terms

Add together '5' and '2'. The expression simplifies to '7 - x'
03

Write the Final Expression

The final expression is presented as '7 - x' after combining like terms

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Key Concepts

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

Combining Like Terms
When simplifying algebraic expressions, one crucial step is combining like terms. It might sound complex, but it's simply about adding or subtracting numbers that belong to the same category. Let's consider the expression from the exercise: \(5 - x + 2\). Here, "5" and "2" are like terms because they are both constants.To combine these like terms, follow these steps:
  • Identify terms that share the same variable. Here, there are no other variables accompanying "x" in the expression.
  • Add or subtract the coefficients of the like terms. For the constants, you add 5 and 2, which gives you 7, as they do not have any variables affecting them.
So, combining these terms simplifies the expression to \(7 - x\). This process of combining like terms helps simplify algebraic expressions, making them more understandable and manageable.
Like Terms
Like terms are an essential part of working with algebraic expressions. They are terms within the expression that have exactly the same variable part. In other words, both the variable and its exponent must match. In the expression \(5 - x + 2\), let's break down the terms:
  • 5 and 2: These are like terms because they are both constants, meaning they do not have any variables attached to them.
  • -x: This is a separate term because it has a variable part "x." If there were another term with an "x," they would be considered like terms and could be combined.
Recognizing like terms is crucial because it allows you to simplify expressions efficiently. When terms are similar, you're able to add or subtract them, which clears clutter and gives a concise expression.
Algebraic Expressions
Algebraic expressions form the backbone of algebra. They are a combination of numbers, variables, and operation symbols. Think of them as mathematical sentences that can convey various relationships.The expression from the exercise, \(5 - x + 2\), illustrates a simple algebraic expression. Here's what's inside:
  • Numbers/Constants: 5 and 2, which represent fixed values.
  • Variables: x, which is a symbol representing a number that can vary.
  • Operators: The minus and plus indicates subtraction and addition operations respectively.
By understanding algebraic expressions, you gain the ability to model real-world situations, solve equations, and analyze mathematical problems. Each component of an algebraic expression plays a significant role in defining its overall property and outcome when simplified or calculated.

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Most popular questions from this chapter

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{75-5^{2}}{11+(3 \cdot 4)} $$

EVALUATING EXPRESSIONS Evaluate the expression. $$ 20+(-16)+(-3) $$

LOGICAL REASONING Decide whether the statement is true or false If false, rewrite the right-hand side of the equation so the statement is true. $$ 7(15-6) \geq 7(15)-7(6) $$

EVALUATING EXPRESSIONS Evaluate the expression. $$ -7+9-8 $$

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 4 w^{2}-w(2 w-3) $$
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