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Inequalities
Chapter 3.3Inequalities
Inequalities are like equations except that in the place
of = we use <,>, ≤, or ≥ .
Treat inequalities exactly as you treat equations , with one important exception.
If you multiply the inequality by a negative number , then you must reverse the
inequality.
Part 1 Graphing inequalities .
The graph will be done on the board.
Question 3 Graph
x≤0
Question 4 Graph
x < 4
Question 12 Solve and Graph
Subtract 5 from both sides
x≥−2
Part 2 Solving inequalities
Question 18: Solve
Subtract 8 from both sides x≥−22
Question 42: Solve
Subtract 2.8x from both sides x < −3.8
If you want to be really proper you can write the solution as
Question 59: Solve −8x ≤ −40
Divide both sides by −8 : [Remember that since we are multiplying/dividing by a negative number that we must reverse the inequality.] x≥5
Question 93: Solve 0.07x < −0.378
Divide by 0.07
So the solution is x < −5.4
Question 124: Solve:
First we simplify by removing parentheses on both sides.
Collect ( Combine ) like terms on each side
10−4y≤6y−20
Subtract 6y from both sides: 10−10y≤−20
Subtract 10 from both sides: −10y≤−30
Divide both sides by −10 . Reverse the inequality.
y≥3
Question 134: Use the roster method to list the set of positive integers that are solutions of the inequality 13−8a≥2−6a
First we solve the inequality :
Add 8a to both sides:
Subtract 2. 11≥2a
Divide by 2 .
Roster method gives us
because , we can’t go any higher than 5.
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