Solving Linear Equations: Variable on One Side: Assignment

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?

x=-1

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?

1. 40x+18(x-3)=468 2. $6

Determine which statements are true. Check all that apply.

1. h(x) has a constant output of -2.50. 3. g(x) is greater than -2.50 for x values less than -1. 6. 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.

C. x=1.5

Noah started to solve the equation -4.6p - 6.3p + 3.9 = -9.18 below. Combine like terms: -10.9p + 3.9 = -9.18 Apply the next steps to solve the equation. What is the solution?

p=1.2

Lorena solved the equation 5k - 3(2k-2/3)-9=0. Her steps are below. 5k - 6k + 2 - 9 = 0 -k - 7 = 0 -k = 7 k=1/7 Analyze Lorena's work to determine which statements are correct. Check all that apply.

1. In Step 1, she correctly distributed -3 to the parentheses. 4. In Step 4, she should have multiplied both sides by-1 to isolate the variable.

On Babylonian tablet YBC 4652, a problem is given that translates to this equation: X+x/7+1/11(x+x/7)=60 What is the solution to the equation?

A. x=48.125

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 15. The modern day equation that models this problem is x+1/4x=15. What is the solution to the equation?

B. x=12

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=10000 If y = 87.5, what is the value for x? 300x +500/7 y = 10,000 300x+500/7(87.5)=10,000 300x+6,250=10,000

x=12.5

If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

x=2/3

Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee? If h represents the hourly fee, which equation models this problem? What was the hourly fee for the rototiller?

1. 7h+43=64 2. $3

Seventy of Myra's classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van. The equation 2b + 6 = 70 represents the given scenario. What does b represent?

C. the number of students who rode on each bus

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)=-72 Which statement is true about Pieter's solution?

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?

C. 14

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?

Sample Answer: Most ancient societies had symbols to represent numbers, but they did not have symbols to represent operations or unknown quantities. Thus, the problems and solutions to the problems had to be written in word form.

Which statements are correct regarding mathematics in the Egyptian, Chinese, and Babylonian cultures? Check all the apply.

1. Both the Egyptian and Chinese number systems use base 10. 3. All three cultures had unique symbolism to represent their numbers. 4. There are two primary sources for ancient Egyptian mathematics.