Download March 21 Compound Inequalities

Warm-up
1.) Which ordered pair is the solution
set for the system of equations below?
2x + y = 18
x – y = –6
(1) (4, 10)
(2) (4, –10)
(3) (8, 3)
(4) (6, 12)
March 21
2.) Determine the quadratic
function whose graph is given
below.
2x + y = 18
x – y = –6
3x = 12
3
3
x=4
2x + y = 18
2(4) + y = 18
8 + y = 18
-8
-8
y = 10
fix
(2, -6)
y = a(x – h)2 + k
y = (x – 1)2 – 7
y = x2 – 2x – 6
HW: Worksheet use pages______
Directions: Write a compound inequality for each solution
set shown below. Then write it in interval notation.
x > −3
x<1
1.
−3 < x < 1
(−3, 1)
Interval notation
2.
x ≤ −2
x>1
−2 ≥ x > 1
(−∞, −2] or (1, ∞)
Interval notation
Interval Notation
Use [ or ] for closed
circle   , 
Use ( or ) for open
circle   , 
Directions:
Graph the solution set of each compound inequality.
3.
[0, 6)
x < 6 and 0 ≤ x  Write as interval notation: _____________
4.
−2) or (5, ∞)
x > −2 or x < 5  Write as interval notation: (−∞,
_____________
5. Solve and graph the solution set of: −10 < 2x – 6 ≤ 8
−10 < 2x – 6 ≤ 8
+6 +6
+6
−4 < 2x ≤ 14
2
2
2
−2 < x ≤ 7
−2
0
2
(−2, 7]
Interval notation
7
6. Solve and graph the solution set of:
8x – 5 > 6x – 1 or 4x ≤ 3x – 7
8x – 5 > 6x – 1 or 4x ≤ 3x – 7
−6x
−6x
−3x −3x
2x – 5 > −1
x ≤ −7
+5 +5
2x > 4
2 2
x>2
−7
0
(−∞, −7] or (2, ∞)
Interval notation
2
7. Solve and graph the solution set of:
−4 ≥ 4(x + 3) ≥ 28
−4 ≥ 4(x + 3) ≥ 28
−4 ≥ 4x + 12 ≥ 28
−12
−12 −12
−16 ≥ 4x ≥ 16
4
4
4
−4 ≥ x ≥ 4
−4
0
(−∞, −4] or (4, ∞)
Interval notation
4
8. Solve and graph the solution set of:
36 > 12 – 3(2x – 4) ≥ 6
36 > 12 – 6x + 12 ≥ 6
36 > 24 – 6x ≥ 6
−24 −24
−24
12 > −6x ≥ −18
−6
−6
−6
−2 < x
≤3
−2
0
3
(−2, 3]
Interval notation
Warm-up
March 21
Warm-up
March 21
1.) Which ordered pair is the solution set for the
system of equations below?
2x + y = 18
x – y = –6
1.) Which ordered pair is the solution set for the
system of equations below?
2x + y = 18
x – y = –6
(1) (4,
(2) (4,
(3) (8,
(4) (6,
(1) (4,
(2) (4,
(3) (8,
(4) (6,
10)
–10)
3)
12)
2.) Determine the quadratic function whose
graph is given below.
10)
–10)
3)
12)
2.) Determine the quadratic function whose
graph is given below.
9. Solve and graph the solution set of:
2x < 6x – 16 or -4(x – 3) > 30 + 2x