1. ALGEBRA
1.6 Inequalities

2. Graph the solution set:
1) x > 5
5x + 2 ≤ 13 for x  {Real Numbers}
5x ≤ 11
x ≤ 11/5
S = {x| x ≤ 11/5, x  R}
3) 5x + 2 ≤ 13 for x  {Integer}
5x ≤ 11
x ≤ 11/5
x ≤ 2
S = {x| x ≤ 2, x  Z} or S = {2, 1, 0, …} -1 1 2

3. Graph the solution set: 4) 3 - 2x ≤ 9 -2x ≤ 6 x ≥ -3 3 < 7
-1(3) ? 7(-1)
-1(3) ? -1(7)
-3 > -7
S = {x| x ≥ -3}
Multiplication Property of Order
If x < y, then If x > y, then
xz < yz, if z is positive xz > yz, if z is positive
xz > yz, if z is negative xz < yz, if z is negative
xz = yz, if z = xz = yz, if z = 0

4. Graph the solution set:
5) | x | < 5
x < x > -5
Can x < 5 and x > -5? Explain?
<  “and”
| x | < 5 means the distance between the origin and x is less that 5 units.
S = { x: -5 < x < 5}

5. Graph the solution set:
5) | x | > 5
x > x < -5
Can x > 5 or x < -5? Explain?
>  “or”
| x | > 5 means the distance between the origin and x is more that 5 units.
S = { x: x < -5 or x > 5}

6. Graph the solution set:
5) | x | < -5
x < x > 5
Can x < -5 and x > 5? Explain?
There are no numbers that are less than -5 and greater than 5
because a number cannot be both negative and positive.
Therefore, S = Ø.

7. Graph the solution set:
5) | 3 - 4x | > 17
3 - 4x > 17
3 - 4x < -17
-4x > 14
-4x < -20
x < -7/2
x > 5
S = { x: x < -7/2 or x > 5}