Inequality
Definitions
Definitions
What are the 4 inequality symbols and what do they represent?
≥ Greater than or equal to
≤ Less than or equal to
> Greater than
< Less than
x - 12 > 0
Add 12 to both sides. Answer: x >12
x ≤ 2
Solid circle at 2, arrow pointing left
See Kumu for Graph #1
x > -7
x + 8 ≥ -5
x ≥ -13 (see kumu for graph & work)
what happens when you multiply or divide an inequality by a negative value?
The inequality sign flips
x + 8 ≤ 43
Subtract 8 from both sides. Answer: x ≤ 35
y < 10
open circle at 10, arrow pointing left
See Kumu for Graph #2
x ≤ 10
-8 ≤ v - 5
*remember keep variable on left!! Answer: v ≥ -3 (see kumu for graph & work)
What does x ≥ 32 mean? Give 2 examples that make this inequality true?
x greater than or equal to 32.
Examples may vary: two examples include 32 (equal to) and 87 (greater than)
15x > 5
Divide both sides by 15.
Answer: x > 5/15 ... simplified to x > 1/3
x ≥ 0
closed circle at 0, arrow pointing right
See Kumu for Graph #3
x < -1
-8x > -72
Answer: x < 9 (see kumu for graph & work)
Explain the difference between a closed & open circle when graphing inequalities.
A closed circle includes the given value in the solution (ex: x≥ 1, x could be values 1 or higher) "greater/less than or equal to"
A open circle does not include the value in the solution (ex: x > 1, x could be values greater than 1, 1 is not included) "greater/lesser than"
Fraction (x/3) > 14
Multiply both sides by 3. Answer: x > 42
m < -4
open circle at -4, arrow to the right
See Kumu for Graph #4
x ≥ 12
fraction (n/-4) > -7
Answer: n < 28 (see kumu for graph & work)
How would draw these graphs?
1) x ≤ 8 2) x > -1
1) Closed circle at 8. Arrow points to the left (aka includes all values to the left of 8, including 8)
2) Open circle at -1. Arrow points to the right (aka includes all values right of -1, not including -1)
-9x ≤ 36
Divide both sides by -9. SIGN FLIP. Answer: x ≥ -4
t ≥ -48
closed circle at -48, arrow to the right
See Kumu for Graph #5
x ≥ -3
fraction (4x/3) > 12
x > 9 (see kumu for graph & work)