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Solving Linear Equations: Variable on One Side, Exams of Mathematics

Miami University - OxfordMathematics

The topic of solving linear equations with variables on one side. It includes several practice problems and solutions related to linear functions, combining like terms, and solving equations. Insights into how ancient cultures, such as egyptian, chinese, and babylonian, approached mathematical problems and their solution methods. It explores the historical context of mathematical development and the evolution of mathematical notation and representation. The document could be useful for students studying algebra, linear equations, and the history of mathematics, particularly those interested in understanding the progression of mathematical problem-solving techniques across different civilizations.

Typology: Exams

2024/2025

Available from 10/17/2024

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Solving Linear Equations: Variable on One Side:
Assignment Test/ Contains 16 Solved
Questions.
The tables given are for the linear functions f(x) and g(x). What is the
input value for which f(x) = g(x) is true? - Answer: x=-1
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x)
is true. - Answer: x=2/3
Noah started to solve the equation -4.6p - 6.3p + 3.9 = -9.18 below.
Combine like terms: -10.9p + 3.9 = -9.18
Page 1 of 6
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Solving Linear Equations: Variable on One Side:

Assignment Test/ Contains 16 Solved

Questions.

The tables given are for the linear functions f(x) and g(x). What is the input value for which f(x) = g(x) is true? - Answer: x=- If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true. - Answer: x=2/ Noah started to solve the equation -4.6p - 6.3p + 3.9 = -9.18 below. Combine like terms: -10.9p + 3.9 = -9.

Apply the next steps to solve the equation. What is the solution? - Answer: p=1. Determine which statements are true. Check all that apply. - Answer: 1. h(x) has a constant output of -2.50.

  1. g(x) is greater than -2.50 for x values less than -1.
  2. The input value for which g(x) = h(x) is between -1 and 0. Use the graph to determine the input value for which f(x) = g(x) is true. - Answer: C. x=1. Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. 7h-5(3h-8)=- Which statement is true about Pieter's solution? - Answer: B. It must be a positive number since it represents a number of hours. Pieter wrote the equation 7h - 5(3h - 8) = -72 to model the number of hours it takes to dig a well to a level of 72 feet below sea level. How many hours will it take to dig the well? - Answer: C. 14
  1. In Step 4, she should have multiplied both sides by-1 to isolate the variable. This week, Michael collected $468 for delivering newspapers. He had 40 repeat customers and 18 new ones. As an incentive, he charged the new subscribers $3 less than the repeat customers. If x represents the amount Michael collects from each repeat customer, which equation models this problem? What is the fee Michael charges each new subscriber? - Answer: 1. 40x+18(x-3)=
  2. $ Problem number 26 of the Rhind Papyrus says: Find a quantity such that when it is added to 1/4 of itself the result is a
  3. The modern day equation that models this problem is x+1/4x=15. What is the solution to the equation? - Answer: B. x= Which statements are correct regarding mathematics in the Egyptian, Chinese, and Babylonian cultures? Check all the apply. - Answer: 1. Both the Egyptian and Chinese number systems use base 10.
  4. All three cultures had unique symbolism to represent their numbers.
  5. There are two primary sources for ancient Egyptian mathematics.

On Babylonian tablet YBC 4652, a problem is given that translates to this equation: X+x/7+1/11(x+x/7)= What is the solution to the equation? - Answer: A. x=48. Chapter 7 of the Jiuzhang suanshu presents a problem of two linear equations involving acres of land and their respective prices. One of the two equations can be translated to: 300x+500/7y= If y = 87.5, what is the value for x? 300x +500/7 y = 10, 300x+500/7(87.5)=10, 300x+6,250=10,000 - Answer: x=12. The types of problems found on ancient papyri, books, and tablets focuses primarily on problems that relate to daily life. The solution methods for many ancient cultures are generally verbal, with mathematical statements written out in words. Why did most ancient cultures primarily write out their mathematical texts in words? - Answer: Sample Answer: