Questions and Answers
What is the algebraic equation for the phrase 'five times the sum of 8u and eight gives one hundred sixty'?
What is the algebraic equation for the phrase 'the difference of fourteen times 7m and seven is ninety-one'?
What is the solution for y in the equation 'the difference of y and eleven gives two'?
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What is the solution for y in the equation 'y plus seven is equal to seventeen'?
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What is the algebraic equation for the phrase 'one times the difference of 6p and one is seventeen'?
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What is the algebraic equation for the phrase 'seventeen times the difference of 15x and twelve is five hundred sixty-one'?
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What is the solution for a in the equation 'twenty-eight subtracted from a gives twenty-two'?
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What is the solution for d in the equation 'subtract twenty-nine from d is eight'?
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Study Notes
Translating Phrases to Algebraic Equations
- Phrase Translation: Understanding key operation words like "times," "difference," and "gives" is essential for translating word phrases into algebraic equations.
- Sum Translation: "Five times the sum of 8u and eight" translates to the equation 5(8u + 8) = 160; parentheses are needed to indicate the sum before multiplication.
- Difference Translation: "The difference of fourteen times 7m and seven" converts to 14(7m) - 7 = 91; recognizing the order of operations is key.
- General Rule: The word "gives" typically means "equals," marking the result of the equation.
Solving Equations
- Difference Example: From the phrase "the difference of y and eleven gives two," we derive y - 11 = 2; solving involves adding 11 to both sides, resulting in y = 13.
- Sum Example: The phrase "y plus seven is equal to seventeen" directly results in y = 10 after isolating y.
- Single Value Example: "One times the difference of 6p and one is seventeen" simplifies to 1(6p - 1) = 17, indicating that the difference is handled within parentheses.
Additional Phrases and Solutions
- Complex Difference: "Seventeen times the difference of 15x and twelve" leads to 17(15x - 12) = 561, emphasizing the need for parentheses around the difference for clarity.
- Subtraction from Variable: "Twenty-eight subtracted from a gives twenty-two" results in a = 50, showcasing rearranging for variable isolation.
- Another Subtraction Example: "Subtract twenty-nine from d is eight" simplifies to d = 37, again illustrating variable solving through addition to find the value.
Key Techniques
- Identify Operations: Always look for keywords signaling operations (addition, subtraction, multiplication).
- Use Parentheses: When dealing with sums or differences being multiplied, always use parentheses to maintain order in operations.
- Solving Process: To isolate the variable, perform inverse operations on both sides of the equation.
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Description
This quiz focuses on translating word phrases into algebraic equations with an emphasis on solving complex problems. It will help you practice identifying operations and forming equations from given phrases. Enhance your algebra skills with these exercises!
