Solving/Interpreting Linear Inequalities in One Step Inequalities

|2x| ≤ 14; Is this an AND or an OR?

• AND

• OR

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

A cyclist rides at an average speed of 31 miles per hour. The cyclist's speed, s, can differ from the average by as much as 8 miles per hour. The absolute value inequalities below can all be used to represent the situation. Which of the following must be the value(s) of x?

• 8

• -8 OR 8

• -8

• -8 AND 8

Solve:

7x - 3x - 8 <= 24

• 8

• -8

• 3.2

• 4

S + 5 > 3

S ?

• > -2

• > 8

• -2

• 8

Distribute and solve:

-2(x+2) < 14

• x < - 5

• x > -5

• x < -9

• x > -9

Solve:
12 - 3p ≥ -5 - 3(p - 8)

• p ≥ -4

• all real numbers

• p ≥ -1

• no solution

Mathematical Equivalence

ON

5x + 5 - 10x < 35

• x < 6

• x > -6

• x > 6

2s ≤ 4 + s