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Questions and Answers
What is the result of evaluating the expression 3x + 4 when x = 2?
What is the result of evaluating the expression 3x + 4 when x = 2?
Which of the following expressions is simplified correctly?
Which of the following expressions is simplified correctly?
If 2x - 5 = 9, what is the value of x?
If 2x - 5 = 9, what is the value of x?
What is the purpose of combining like terms in an expression?
What is the purpose of combining like terms in an expression?
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Which property allows you to add the same number to both sides of an equation?
Which property allows you to add the same number to both sides of an equation?
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What is the result of the operation 2(x + 3) + 4x?
What is the result of the operation 2(x + 3) + 4x?
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What is a variable in a mathematical expression?
What is a variable in a mathematical expression?
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If you simplify 3x + 4x - 2y + 5y, what is the final expression?
If you simplify 3x + 4x - 2y + 5y, what is the final expression?
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Study Notes
Variables and Expressions
- Variables represent unknown values in mathematical expressions. They are often letters like
x,y, orz. - Algebraic expressions combine variables, numbers, and operations (addition, subtraction, multiplication, division).
- Example:
2x + 5is an algebraic expression.
Evaluating Expressions
- To evaluate an expression means to find its value when the variables are given specific values.
- Substitute the given values for the variables in the expression.
- Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
- Example: If
x = 3in the expression2x + 5, substitute3forx:2(3) + 5 = 6 + 5 = 11.
Combining Like Terms
- Like terms are terms that have the same variables raised to the same powers.
- Combine like terms by adding or subtracting their coefficients.
- Example: In the expression
3x + 2x, the terms3xand2xare like terms, so3x + 2x = 5x.
Simplifying Expressions
- Simplifying an expression means writing it in its most basic form.
- Distribute terms by multiplying the term outside the parentheses to each term inside. This may involve combining like terms.
- Combine like terms to ensure there are no more like terms to group.
- Example:
2(x + 3) + 4xbecomes2x + 6 + 4x = 6x + 6
Solving Equations (Basic)
- An equation is a statement that two expressions are equal.
- To solve an equation means finding the value of the variable that makes the equation true.
- The goal in solving simple equations is to isolate the variable. Use inverse operations.
- Example: To solve
x + 3 = 7, subtract 3 from both sides to getx = 4.
Properties of Equality
- Additive Property of Equality: Adding the same quantity to both sides of an equation does not change the solution.
- Subtraction Property of Equality: Subtracting the same quantity from both sides of an equation does not change the solution.
- Multiplication Property of Equality: Multiplying both sides of an equation by the same quantity (except zero) does not change the solution.
- Division Property of Equality: Dividing both sides of an equation by the same quantity (except zero) does not change the solution.
Real-World Applications
- Algebraic expressions and equations model real-world scenarios.
- For instance, finding the total cost of items (with different prices), calculating distances traveled, or figuring out time taken.
- Understand how to translate word problems into algebraic expressions and equations.
Exponents and Powers
- Exponents show repeated multiplication.
- Example:
x³meansx × x × x. - Understand the relationship between exponents and powers.
- Know the rules of exponents, including
x^2*x^3=x^5(product of powers rule).
Introduction to Polynomials
- Polynomials are algebraic expressions with multiple terms.
- Examples of Polynomials:
2x² + 3x - 1,5y,y^3-y.
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Description
Test your understanding of algebraic variables and expressions. This quiz covers evaluating expressions, substituting values, and combining like terms with hands-on examples. Boost your skills in simplifying and solving algebraic expressions effectively.
