7.5 linear inequalities. 7.5 – linear inequalities goals / “i can…” graph linear...
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7.5
Linear Inequalities
7.5 – Linear Inequalities
Goals / “I can…”Graph linear inequalitiesWrite and use linear inequalities when modeling
real – world situations
7.5 – Linear Inequalities
RECALLRECALLGraph x > 4 on a number line.
Graph y ≤ 2 on a number line.
0 2 4-2-4
0 2 4-2-4
7.5 – Linear Inequalities
REMEMBER:The type of dot on the number line is
important. OpenOpen DOT means NOT INCLUDED (> or <> or <)ClosedClosed DOT means INCLUDED (≤ or ≥≤ or ≥)
Remember these symbols!!!!
Less than
Greater than
Less than or EQUAL TO
Greater than or EQUAL TO
7.5 – Linear Inequalities
When graphing inequalities on the coordinate plane, we use a similar idea. Dashed linesDashed lines mean the same as open circles.
(> or <> or <)
Solid lines meanSolid lines mean the same as closed circles. (≤ or ≥≤ or ≥)
Graphing an Inequality in Two Variables
Graph x < 2Step 1: Start by graphing the line x = 2
Now what points would give you less
than 2?
Since it has to be x x << 2 2 we shade everything to
the left of the line.
7.5 – Linear Inequalities
Oh, and did I mention we have to shade a part of the graph?????
When considering shading, you shade the part of the graph that WORKS FOR THE WORKS FOR THE EQUATIONEQUATION.
Graphing a Linear Inequality
Sketch a graph of y 3
7.5 – Linear Inequalities
Graph
x ≥ 3x ≥ 3
7.5 – Linear Inequalities
Graph
y ≤ 2x + 2y ≤ 2x + 2
Solving an Inequality
Solving a linear inequality in one variable is much like solving a linear equation in one variable. Isolate the variable on one side using inverse operations.
Add the same number to EACH side.
x – 3 < 5Solve using addition:
53 x+3 +3
x < 8
Solving Using Subtraction
Subtract the same number from EACH side.
106 x
4x-6 -6
THE TRAP…..
When you multiply or divide each side of an inequality by a negative negative numbernumber, you must REVERSE the inequality SYMBOL to maintain a true statement.
Solving by multiplication of a negative #
Multiply each side by the same negative number and REVERSE the inequality symbol.
4 x Multiply by (-1).
4x
(-1) (-1)
See the switch
Solving by dividing by a negative #
Divide each side by the same negative number and reverse the inequality symbol.
62 x
3x
-2 -2
Solving using Multiplication
Multiply each side by the same positive number.
32
1x
6x
(2) (2)
Some Helpful Hints•If the sign is > or < the line is
dashed
•If the sign is or the line will be solid
When dealing with just x and y.
•If the sign > or the shading either goes up or to the right
•If the sign is < or the shading either goes down or to the left
Using What We KnowSketch a graph of x + y < 3
Step 1: Put into slope intercept form
y < -x + 3
Step 2: Graph the line y = -x + 3
When dealing with slanted lines
•If it is > or then you shade above
•If it is < or then you shade below the line