Questions and Answers
What is the solution to the equation $3x + 4 = 13$?
x = 3
What is the solution to the equation $x - 5 = 23$?
x = 28
What is the value of x when solving the system of equations $y = 3x + 2$ and $y = 6x - 1$?
x = 1
What are the factored forms of the expression $x^2 + 4x + 3$?
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What are coefficients in algebra?
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What are constants in algebraic expressions?
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What do variables represent in algebraic expressions?
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Study Notes
Solving Linear Equations
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To solve the equation 3x + 4 = 13, first isolate the variable by subtracting 4 from both sides, resulting in 3x = 9.
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Dividing both sides by 3 gives the solution: x = 3.
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For the equation x - 5 = 23, add 5 to both sides to find x = 28.
Systems of Equations
- Given the equations y = 3x + 2 and y = 6x - 1, set them equal to each other: 3x + 2 = 6x - 1.
- Rearranging yields 3x = 3 after moving all variable terms to one side and constants to the other.
- Solution for x is found by dividing both sides by 3, leading to x = 1.
Factoring Quadratic Expressions
- The expression x^2 + 4x + 3 can be factored as (x + 1)(x + 3).
Key Algebraic Terms
- Coefficients represent the numerical factor in terms with variables (e.g., in 3x, the coefficient is 3).
- Constants are numbers without variables in algebraic expressions; they do not change.
- Variables are represented by letters in algebra, symbolizing numbers that can vary.
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Description
Test your knowledge on solving linear equations, systems of equations, and factoring quadratic expressions. This quiz covers key algebraic terms and the steps necessary to find solutions. Perfect for reinforcing your algebra skills!
