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Questions and Answers
What is the definition of a term in algebra?
What is the definition of a term in algebra?
- A mathematical expression that includes only constants.
- A factor that multiplies a variable.
- A single mathematical expression such as a number or variable. (correct)
- An equation that contains variables.
Which of the following pairs of terms can be combined because they are like terms?
Which of the following pairs of terms can be combined because they are like terms?
- 6z and -2z (correct)
- x and x²
- 2x² and 5x² (correct)
- 3x and 4y
When utilizing the distributive law on the expression 4(3x + 5), which of the following is the correct result?
When utilizing the distributive law on the expression 4(3x + 5), which of the following is the correct result?
- 4x + 20
- 12x + 15
- 12x + 20 (correct)
- 4x + 15
What is the correct result of the expression 5x - (2x + 3)?
What is the correct result of the expression 5x - (2x + 3)?
What is the first step in solving a linear equation with parentheses?
What is the first step in solving a linear equation with parentheses?
In the linear equation form aX + B = 0, what restriction applies to the value of 'a'?
In the linear equation form aX + B = 0, what restriction applies to the value of 'a'?
Which of the following correctly illustrates the use of the order of operations (PEMDAS) for the expression 3 + 4 × (2 - 1)²?
Which of the following correctly illustrates the use of the order of operations (PEMDAS) for the expression 3 + 4 × (2 - 1)²?
Flashcards
Term
Term
A single mathematical expression that can be a number, a variable, or their combination (e.g., 5, -3, 12, 4x).
Like Terms
Like Terms
Terms that have the same variable raised to the same power (e.g., 3x and 5x, 2x² and -4x²).
Unlike Terms
Unlike Terms
Terms that have different variables or different exponents (e.g., 2x and 3y, x and x²).
Coefficient
Coefficient
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Distributive Law
Distributive Law
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Adding and Subtracting Linear Expressions
Adding and Subtracting Linear Expressions
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Factorization
Factorization
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Order of Operations (PEMDAS)
Order of Operations (PEMDAS)
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Study Notes
Algebra Concepts
- Terms: Single mathematical expressions (numbers, variables, or combinations); examples include 5, -3, 4x, x².
- Constants: Terms without variables; examples include 5, -3, 12.
- Coefficients: Numerical factors multiplying variables; example, 4 in 4x.
- Like Terms: Share the same variable raised to the same power; examples: 3x and 5x; 2x² and -4x².
- Unlike Terms: Have different variables or exponents; examples: 2x and 3y; x and x².
- Distributive Law: a(b + c) = ab + ac; used to distribute coefficients across sums or differences within parentheses; examples: 3(x + 2) = 3x + 6; 2(2x - 4) = 4x - 8.
- Addition and Subtraction of Linear Expressions: Combine like terms; examples: 3x + 4x + 2 = 7x + 2; 5x - (2x + 3) = 3x - 3.
- Factorization: Breaking down an expression into simpler factors; factoring out the Greatest Common Factor (GCF) is common; example: 6x² + 9x = 3x(2x + 3).
- Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Example: 3 + 4 × (2 - 1)² = 7.
Equations
- Equation: Shows a relationship between variables using an equal sign. Distinguishable from an expression.
- Handling Parentheses: Remove parentheses first before solving equations.
Solving Word Problems with Linear Equations
- Step 1: Identify the unknown.
- Step 2: Assign a variable (e.g., X) to the unknown.
- Step 3: Express known quantities in terms of the variable.
- Step 4: Write an equation based on the problem's conditions.
- Step 5: Solve the equation.
- Step 6: State the answer clearly.
Linear Equations in One Variable
- Form: aX + B = 0, where 'a' and 'B' are constants, and 'a' ≠0.
Methods for Solving Linear Equations
- Add a term to both sides.
- Subtract a term from both sides.
- Multiply both sides by a constant.
- Divide both sides by a constant.
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