# Graphing and Solving Equations and Inequalities

1) Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all of your work:

a) 2x + 5 = 9

Answer: x=2

Show your work here: 2x=9-5

X=4/2

X=2

b)

Answer: x=-3

Show your work here: -6x - 6+4= 16

-6x-2 = 16

X= -18/6

X= -3

c)

Answer: x=60

Show your work here: 12[ 3/4x-5] = 12 [ 2/3 x]

9x-60=8x

9-8x= 60

X=60

d)

Answer:

Show your work here:

2) a) Solve for y

Answer:

Show your work here:

b) When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

Slope = ______

Y-intercept = _____

c) Using your answer from part a, find the corresponding value of y when x =12.

Answer:

Show your work here:

3) The following graph shows Bob's salary from the year 2002 to the year 2005. He was hired in the year 2002; therefore x = 0 represents the year 2002.

a) List the coordinates of any two points on the graph in (x, y) form.

(_1, _2_),(_2_, _3_)

b) Find the slope of this line:

Answer: 1

Show your work here: m= 3-2/ 2-1= 1

c) Find the equation of this line in slope-intercept form.

Answer: y= 1x + 1

Show or explain your work here: y=mx+b 2-1=b

Y=1(x)+b 1=b

2= 1(1)+b

d) Using the result in part c, determine Bob's salary, in dollars, in 2008.

Answer:

Show or explain your work here:

4) Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78.

a) Set up an equation involving only W, the width of the rectangle.

Answer:

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well. Use the appropriate units of measure in you answers.

Answer: Length ______, Width ______

Show your work here:

5) A tennis club offers two payment options:

Option1: $35 monthly fee plus $4/hour for court rental

Option 2: No monthly fee but $6.50/hour for court rental.

Let x = hours per month of court rental time.

a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

Option 1: C=_________________

Option 2: C=_________________

b) How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2. Set up an inequality and show your work algebraically using the information in part a.

Answer:

Show your work here:

6) Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.

If you were to connect these points with a line, where would the y-intercept be located? Give answer in (x, y) form.

(___, ___)

© BrainMass Inc. brainmass.com October 16, 2018, 10:40 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/graphing-and-solving-equations-and-inequalities-228868

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

MTH133

Unit 1 Individual Project -

Name:

1) Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all of your work:

a) 2x + 5 = 9

Answer: x=2

Show your work here: 2x=9-5

X=4/2

X=2

b)

Answer: x = -3

Show your work here: -6x - 6+4= 16

-6x - 2 = 16

-6x = 18

x = -18/6

x = -3

c)

Answer: x=60

Show your work here: 12[ 3/4x-5] = 12 [ 2/3 x]

9x-60=8x

9x - 8x= 60

x =60

d)

Answer: x < -4

Show your work here:

Subtract 4 from each side, we will get

-2x > 12 -4

-2x > 8

Divide each side by -2, we will get

x < -4 (when we divide by a negative number in ...

#### Solution Summary

A step by step solution to all the problems is proided.

Algebra: Solving equations, graphing, inequalities, word problems.

15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below.

a). Use the two points reporting data for 9 hours of study time and 23 hours of study time and find a linear function that fits the data. (You can ignore the other lines of data in the chart.)

b.) Use the function to predict the test score of someone who has studied for 18 hours.

Study Time, x (in hours) Test Grade, y (in percent)

9 74

11 94

13 81

15 86

16 87

17 81

21 87

23 92

16. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

Josh left a 15% tip for a meal. The total cost of the meal, including the tip, was $30.50. What was the cost of the meal before the tip was added?

17. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

The product of two consecutive odd integers is 255. Find the integers.

18. Define your variables and write a system of equations that could be used to solve the following problem. Do not solve the equations.

Madeline goes to a bank and gets change for a $50 bill consisting of all $5 bills and $1 bills. There are 22 bills in all. How many of each kind are there?

19. Solve 3(r - 6) + 2 > 4(r + 2) - 21 and express the solution as a graph, using solution set notation, and using interval notation.

20. Graph 2x + 3y ≥ 6.

View Full Posting Details