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Chapter 3: Problem 19

Identify as an expression or an equation. $$8 x-9-7$$

Short Answer

Expert verified
Expression

Step by step solution

01

Identify the terms

Look at the given problem: \(8x - 9 - 7\). Identify the different parts or terms in this problem. The terms are \(8x\), \(-9\), and \(-7\).
02

Check for equality sign

An equation has an equality sign (\(=\)) that shows that two expressions are equal. There is no equality sign in \(8x - 9 - 7\).
03

Verify if it can be simplified further

Combine like terms if possible. In this case, combine \(-9\) and \(-7\): \(8x - 16\). Simplification does not convert the expression into an equation.
04

Conclusion

Since there is no equality sign and it consists of terms without declaring equality to another value or expression, this is an algebraic expression.

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Key Concepts

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

Expressions vs. Equations
The primary distinction between an expression and an equation is the presence of an equality sign (=).

  • An expression is a combination of numbers, variables, or both, without an equality sign. For instance, 8x - 9 - 7 is an expression because it only combines terms without showing equality.

  • An equation shows two expressions are equal with an equality sign. For example, 8x - 9 - 7 = 0 is an equation because it asserts that 8x - 9 - 7 equals zero.
Understanding the difference helps with categorizing algebraic problems correctly and solving them appropriately.
Combining Like Terms
Combining like terms simplifies expressions, making them easier to work with. Here鈥檚 how to do it:

  • Identify like terms: Like terms contain the same variables raised to the same power. In our example, 8x, -9, and -7 are terms.

  • Combine constants: Constants are terms without variables. Add or subtract them, such as -9 and -7, which combine to give -16.

  • Write the simplified expression: After combining, re-write the expression. Our example becomes 8x - 16.
By combining like terms, we reduce complexity, making it easier to handle algebraic expressions in further steps.
Simplifying Expressions
Simplifying expressions means making them as concise as possible. Follow these steps:

  • Combine like terms: This step was covered in the previous section, where 8x - 9 - 7 simplifies to 8x - 16.

  • Eliminate parentheses: If any parentheses exist, use the distributive property to remove them. This isn't required in our example.

  • Check for common factors: If terms share common factors, factor them out. This isn't applicable in our example, but it鈥檚 good practice to check.

  • Simplify the expression: If additional simplifications are possible, perform them. Ensure that the final expression is in its simplest form. Our example results in 8x - 16.
Simplifying makes expressions easier to understand and use in subsequent algebra operations or problem-solving.

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Most popular questions from this chapter

Demonstrate the associative property of addition by evaluating the expressions for \(a=-4, b=-6,\) and \(c=18\). a. \((a+b)+c\) b. \(a+(b+c)\)

Apply the distributive property. $$-2(-10 p-12 q+3)$$

Demonstrate the commutative property of multiplication by evaluating the expressions for \(x=-9\) and \(y=5\). a. \(x \cdot y\) b. \(y \cdot x\)

Combine the like terms. $$-5-11 p+23 p-p+4$$

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