Questions and Answers
What is the equation that describes the relationship where the difference of f and five times g is the same as 25 minus f?
f - 5g = 25 - f
What formula represents the perimeter of a rectangle?
P = 2l + 2w
What is the algebraic expression for 'j plus 16 is 35'?
j + 16 = 35
What is the solution for v in the equation v - 9 = 14?
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What is the solution for c in the equation c/4 = -9/8?
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What is the solution for x in the equation x/9 = 10?
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What is the solution for v in the equation -v/5 = -45?
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What is the solution for t in the equation 3t + 7 = -8?
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What is the solution for x in the equation 9x + 27 = -72?
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What is the solution for c in the equation 7c + 12 = -4c + 78?
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What is the solution for a in the equation 6(3a + 1) - 30 = 3(2a - 4)?
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What is the result when evaluating 4a - |3b + 2c| for a = -2, b = -3, and c = 2?
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What is the result when evaluating 3|3b - 8c| - 3 for a = -2, b = -3, and c = 2?
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What are the solutions for n in the equation |n - 3| = 5?
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What is the solution for the equation |v - 2| = -5?
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What are the solutions for t in the equation |4t - 8| = 20?
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Are the ratios 9/11 and 81/99 equivalent?
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Are the ratios 4/3 and 6/8 equivalent?
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What is the value of 'a' in the equation 3/8 = 15/a?
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What is the value of 'g' in the equation 15/35 = g/7?
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Study Notes
Algebraic Expressions and Equations
- f-5g==25-f: Represents the equation stating the difference between f and five times g equals 25 minus f.
- P=2l+2w: Formula for the perimeter of a rectangle, where P is perimeter, l is length, and w is width.
Solving Equations
- j + 16 = 35: Equation indicating that j added to 16 equals 35.
- v - 9 = 14: Solving yields v = 23.
- c/4 = -9/8: Solving gives c = -9/2.
- x/9 = 10: Results in x = 90.
- -v/5 = -45: Solutions lead to v = 225.
- 3t + 7 = -8: Simplifying yields t = -5.
- 9x + 27 = -72: Results in x = -11.
- 7c + 12 = -4c + 78: Yields c = 6.
- 6(3a + 1) - 30 = 3(2a - 4): Results in a solution of a = 1.
- Evaluate 4a - |3b + 2c| for a = -2, b = -3, c = 2 leads to -13.
Absolute Value and Evaluations
- Evaluate 3|3b - 8c| - 3 with a = -2, b = -3, c = 2 yields 72.
- |n - 3| = 5: The solutions are {8, 2}, indicating possible values for n.
- |v - 2| = -5: This has no solution as absolute values cannot be negative.
- |4t - 8| = 20 results in t values of {7, -3}.
Ratios and Proportions
- Are 9/11 and 81/99 equivalent?: Yes, they simplify to the same value.
- Are 4/3 and 6/8 equivalent?: No, they simplify to different values.
Additional Problem Solutions
- 3/8 = 15/a leads to a solution of a = 40.
- 15/35 = g/7 leads to a solution g = 3.
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