MTH 103 Group Activity Problems (W3B) Name: Linear Equations Section 2.2 (Due April 20)

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1 MTH 103 Group Activity Problems (W3B) Name: Linear Equations Section 2.2 (Due April 20) Learning Objectives Learn about equations and recognize a linear equation Solve linear equations symbolically Solve linear equations graphically and numerically Apply problem solving strategies Definition: A linear equation in one variable is an equation that can be written in the form are constants and If an equation does not fit the definition of a linear equation then it is a nonlinear equation. a Compare each equation below to the definition of a linear equation. Circle each equation that is a linear equation. Then identify the values of a and b. For each equation that is nonlinear, write an explanation of why it is nonlinear. a. 4 5x 3 b. 3 x 7 0 ax b 0 where a and b c. 6 7 p d. 4t 11t e x 13 4x x f Is the value x 3 a solution to the equation 4x 9 14x 5? Without doing work to solve the equation, explain verbally how you can check whether or not it is a solution, and include work with your explanation. To find an exact solution to a linear equation, we can solve the equation symbolically, writing our work one step at a time to transform the equation into an equivalent equation that is simpler. When we have simplified to the form x a number, then we have found the solution to the original equation. 3. Solve each linear equation symbolically to find an exact solution. Make sure to show (write out) all steps of your work, neatly and in the order you do them, so that your work can easily be followed by another person. a. 9x 3 24 After you solve, check your work using the ideas you explained in problem #2. Show your check here:

2 b. 32t 1 2t Check: 3 5 p p 2 7 p c. 2 Check: d. k k Tip: When solving a linear equation that contains fractions, it can help to first multiply each side of the equation by the least common denominator of all the fractions. We call this technique eliminating, or clearing, fractions. You can review finding an LCD on page R-30 in your textbook. Check:

3 3x 1 2 x e f. 1.1c c 2 g. (x 1) + 3 = 1 2 ( 2x) + 4 h. 3(x 1) 2x = x 6

4 In addition to finding exact solution by solving symbolically, we can also estimate solutions graphically and numerically. 2 f x x 3 Values in the table have been rounded to five decimal places. 4. A graph and table are shown for the linear function 8 a. Explain in detail how you could use the graph to solve the equation 2 x x y b. Explain in detail how you could use the table to solve the equation 2 x 8 5 3

5 Solve each problem symbolically, showing all your work and explaining your reasoning. Remember to check each answer. f x x Tuition and fees during year x at a private college can be modeled by 6121 a. Use f x to determine when tuition and fees might reach $28,000. b. Write your final answer using function notation and explain in words what your answer means. 6. In order to receive an A in a college course it is necessary to obtain an average of 90% correct on three exams of 100 points each and a final exam of 200 points. If a student scores 82, 88 and 91 on the first three exams, what is the minimum score that the person can receive on the final exam and still earn an A? 7. Andrew and Peter just graduated from college and are starting new jobs this month. Andrew was given a signing bonus of $5000 and will earn a monthly salary of $4000. Peter decided to take a job where he did not get a signing bonus, but will earn a monthly salary of $4600. a. Write a formula for the function A(m) which inputs the number of months worked and outputs the total amount of money Andrew has been paid. b. Write a formula for the function P(m) which inputs the number of months worked and outputs the total amount of money Peter has been paid. c. How many months will pass before Peter will have earned more money than Andrew?

6 8. A 174-foot-long fence is being placed around the perimeter of a rectangular swimming pool that has a 3-foot-wide sidewalk around it. The actual swimming pool without the sidewalk is twice as long as it is wide. Find the dimensions of the pool without the sidewalk. 9. A company manufactures CDs. The master disc costs $2000 to produce and copies cost $0.45 each. If the company spent $2990 producing a particular CD, how many copies did the company manufacture? 10. Formaldehyde is an indoor air pollutant found in building materials. When concentrations in the air reach 33 micrograms per cubic foot, g 3, eye irritation can occur. One square foot of new plywood could emit 140 ft formaldehyde per hour. g of a. A room has 100 square feet of new plywood flooring. Find a linear function f(t) that computes the amount of formaldehyde in that could be emitted in t hours. g b. The room contains 800 cubic feet of air and has no ventilation. Determine how long it would take for concentrations g to reach a dangerous level of Write your final answer using function notation. ft