Download Graphing Inequalities Classwork/Notes

Graphing Inequalities Classwork/Notes
Only selected questions have answers, one question on each topic is answered. If the
problem you are stuck on doesn’t have an answer, look at the bold numbers in purple,
that number is the problem that can help you.
1.) Thelma and Laura start a lawn-mowing business and buy a lawnmower for $225. They
plan to charge $15 to mow one lawn. What is the minimum number of lawns they need to
mow if they wish to earn a profit of at least $750?
1. Make an equation: 15x = 225+750 (you have to add 225 to 750 because they want to make
750 and first they have to get rid of their expenses.
2. Solve the equation like you would any other:
15x = 225+750
15x = 975
15
15
x = 65 lawns
2.) Which inequality is represented in the accompanying graph?
open ( o ) = > or <
closed ( ) = > or <
1. Write in the numbers around x, as shown : -3 x 4
2. Fill in the blanks: -3 < x <
* Helpful hint: as Ms. Bigelow says, they should never “Batman Dance” the symbols should
always be going in the same direction.
3.) In order to be admitted for a certain ride at an amusement park, a child must be greater
than or equal to 36 inches tall and less than 48 inches tall. Draw a graph represents these
conditions?
1. Look for numbers and words that could translate into symbols, I’ve highlighted ones I saw.
2. Start by making the graph with only numbers on it:
3. Now decide whether the dot should be open or closed and fill in the middle:
4.) Which graph represents the solution set for 2x - 4  8 and x + 5  7 ?
(1)
(2)
(3)
(4)
Look at number 2 for help.
5.) Which point is in the solution set of the system of inequalities shown in the accompanying
graph?
(1) (0,4)
(3) (–4,1)
(2) (2,4)
(4) (4, –1)
Plot the point, the one in the cross
checkered area is correct:
(4,-1)
6.) Solve: 3x + 4y > -24
Look at the first parts of 7.
7.) Graph the following systems of inequalities on the accompanying set of axes and label the
solution set S:
1. Make the equations into mx+b
form.
y+2x > -4
2. Graph the lines, remember a
-2x
-2x
dashed line means < or > and a
y > -2x -4
solid line means < or >.
3. Use the point (0,0) in the
x < 18- 9y
equation to decide which way to
-18 -18
shade.
x-18 < -9y
0 >-2 (0) -4 , 0> 0 -4 , 0> -4
-9
-9
shade towards the point (0,0)
- 1 x -2 < y
9
0>-1 (0) – 2 , 0> 0-2 , 0> -2
9
8.) Does the point (9, 8) lie on the line y=1/3x + 5?
Since the equation is already in mx+b form, simply put the point into the equation:
8= 9 + 5
3
8=3 + 5
8= 8
The point is on the line.
9.) Does the point (1, 2) lie on a circle with radius 2 and center at (-1, 0)?
Use the circle equation: (x-a)2 + (y-b)2= R2 It isn’t on the line because the solution
(1+1)2 + (2-0)2= 22 is false.
(2)2 + (2)2 = 22
4+4=4
8=4
10.) Does the point (3, -4) lie on the line 4y + -3x = 0?
Look at number 8.
11.) Graph the solution to -8x + 2 > 26
Look at number 3.