Questions and Answers
Complete the equation describing how x and y are related: Y = ?x + ?
5x, 3
Complete the equation describing how x and y are related: y = ?x + ?
4x, -1
Complete the equation describing how x and y are related: Y = ?x + ?
-2x, 1
Complete the equation describing how x and y are related: y = ?x
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Complete the equation describing how x and y are related: y = ?x + ?
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Complete the equation describing how x and y are related: y = x + ?
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Complete the equation describing how x and y are related: y = x + ?
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Combine like terms: 8y - 4z + 3y + 5z = ?y + ?z
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Use the distributive property: 3(4x - 9) = ?x + ?
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Combine like terms: 9y + 5y - 3 = ?y + ?
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Combine like terms: 3x - 7x = ?x
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Use the distributive property: 4(5x + 3y - 7) = ?x + ?y + ?
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Use the distributive property: 6(3x - 4y + 7z) = ?x + ?y + ?z
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Combine like terms: 4x - 7y + 2x - 4 = ?x + ?y + ?
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Evaluate and simplify the expression when a = 2 and b = 4: 4a - 2(a + b) + 1 = ?
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Evaluate and simplify the expression when x = 1 and y = 2: ?
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Evaluate and simplify the expression when a = 3 and b = 2: 3b - 2(1-b) / a - 2 = ?
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Evaluate and simplify the expression when a = 2 and b = 1______: 20a - 1 / b = ?
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Evaluate the expression when m = 25: m + 2(m-5) = ?
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Evaluate and simplify the expression when x = 14 and y = 1/3: 2x ?/ 13 - 9y = ?/?
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Evaluate and simplify the expression when a = 2 and b = 4: 4a + 2b^2 - 2(a - 3b) = ?
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Solve the equation and give your simplified answer as an improper fraction: -4(3 + x) + 5 = 4(x + 3)
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Solve the equation: -2(4 + 3x) = 3(x - 2)
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Solve the equation and give your simplified answer as an improper fraction: 4(x + 5) = 6(2x - 1)
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Solve the equation and give your simplified answer as an improper fraction: 3(x - 2) + 6 = 4(2 - x)
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Solve the equation and give your simplified answer as an improper fraction: -(x - 1) + 10 = -3(x - 2)
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Solve the equation: 10x - ______(x + 5) = 4x - ______
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Solve the equation: 5x - (x + 3) = 3(2 - 2x) + x
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The number 0 is a solution to: -4 _ ?
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Solve the inequality: 4 _ ?
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Study Notes
Equations of Lines: Slope-Intercept Form
- The relationship between x and y can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.
- For the dataset {X: -1, 0, 1, 2, 3, 4, 5} and {Y: -2, 3, 8, 13, 18, 23, 28}, the equation is Y = 5x + 3.
- For {X: 0, 1, 2, 3, 4} and {Y: -1, 3, 7, 11, 15}, the equation becomes y = 4x - 1.
- For {X: 0, 1, 2, 3, 4, 5} and {Y: 1, -1, -3, -5, -7, -9}, the equation is Y = -2x + 1.
- Given the relationship {X: -2, -1, 0, 1, 2, 3} and {Y: -4, -2, 0, 2, 4, 6}, the equation simplifies to y = 2x.
- For the dataset {X: 0, 1, 2, 3, 4, 5} and {Y: 7, 9, 11, 13, 15, 17}, the equation is y = 2x + 7.
- For {X: 0, 1, 2, 3, 4, 5, 6} and {Y: 5, 6, 7, 8, 9, 10, 11}, the equation is y = x + 5.
- Given {X: 1, 2, 3, 4, 5, 6} and {Y: -4, -3, -2, -1, 0, 1}, the resulting equation is y = x - 5.
Combining and Simplifying Expressions
- Combining like terms: 8y - 4z + 3y + 5z simplifies to 11y + z.
- Using the distributive property with 3(4x - 9) results in 12x - 27.
- Combining terms 9y + 5y - 3 simplifies to 14y - 3.
- The expression 3x - 7x simplifies to -4x.
- Distributing 4(5x + 3y - 7) results in 20x + 12y - 28.
- For 6(3x - 4y + 7z), results are 18x - 24y + 42z.
- Combining 4x - 7y + 2x - 4 gives 6x - 7y - 4.
Evaluating Expressions
- Evaluating 4a - 2(a + b) + 1 with a = 2 and b = 4 yields -3.
- For x = 1 and y = 2, the expression evaluates to 23.
- Simplifying 3b - 2(1 - b) / a - 2 using a = 3 and b = 2 gives 8.
- Evaluating 20a - 1 / b with a = 2 and b = 13 results in 3.
- When m = 25, the expression m + 2(m - 5) evaluates to 65.
- For x = 14 and y = 1/3, the expression 2x / 13 - 9y evaluates to 14/5, or 2.8.
- Evaluating 4a + 2b^2 - 2(a - 3b) with a = 2 and b = 4 results in 60.
Solving Equations
- Solving the equation -4(3 + x) + 5 = 4(x + 3) results in x = -19/8.
- From -2(4 + 3x) = 3(x - 2), x simplifies to -2/9.
- The equation 4(x + 5) = 6(2x - 1) gives x = 13/4.
- In 3(x - 2) + 6 = 4(2 - x), x equals 8/7.
- Solving -(x - 1) + 10 = -3(x - 2) leads to x = -5/2.
- The equation 10x - 2(x + 5) = 4x - 2 results in x = 2.
- For 5x - (x + 3) = 3(2 - 2x) + x, x simplifies to 1.
Analyzing Zero Solutions and Inequalities
- The condition 0 = -4 can imply specific values of x when paired with factors like -7/3 and 5.
- Inequalities such as 4 suggest solutions could fall into specific ranges.
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Description
Test your understanding of linear equations in the Acellus Algebra 2 course. This quiz challenges you to complete equations that describe the relationship between x and y based on given data points. Sharpen your algebra skills and reinforce your knowledge of equations in a fun way.
