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Inequalities Review
• Agenda
– Review Inequalities
– Begin Homework
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P 570 (2-20 evens)
P 574 (5-9 & 43-51 odds)
P 576 (20-24 evens)
Study for Practice CST which starts tomorrow!
Solving Inequalities Using Addition and Subtraction
Solve 8 > d – 2. Graph and check your solution.
8+2>d–2+2
10 > d, or d < 10
Check: 8 = d – 2
8
10 – 2
8=8
8 ≥ d–2
8 ≥ 9–2
8 ≥ 7
Add 2 to each side.
Simplify.
Check the computation.
Substitute 10 for d.
Check the direction of the inequality.
Substitute 9 for d.
Quick Check
Solving Inequalities Using Addition and Subtraction
Solve c + 4 > 7. Graph the solution.
c+4–4>7–4
c>3
Subtract 4 from each side.
Simplify.
Quick Check
Solve and graph the inequalities.
x
1) 4x  20
2)
 2
3
4x  20
x
(3)  2(3)
4 4
3
x 5
x  6
0
5
-6
0
6
1) 4x  24
4x  24
4  4
x  6
-6
y
2)
7
3
y
(3)
 7(3)
3
y  21
0
-21
0
Solving Multi-Step Inequalities
Solve 8z – 6 < 3z + 12.
8z – 6 – 3z < 3z + 12 – 3z
Subtract 3z from each side.
5z – 6 < 12
Combine like terms.
5z – 6 + 6 < 12 + 6
Add 6 to each side.
5z < 18
Simplify.
5z
18
<
5
5
Divide each side by 5.
3
z < 35
Simplify.
Quick Check
Solving Multi-Step Inequalities
Solve 5(–3 + d) < 3(3d – 2).
–15 + 5d < 9d – 6
–15 + 5d – 9d < 9d – 6 – 9d
Use the Distributive Property.
Subtract 9d from each side.
–15 – 4d < –6
Combine like terms.
–15 – 4d + 15 < –6 + 15
Add 15 to each side.
–4d < 9
Simplify.
–4d
9
>
–4
–4
Divide each side by –4. Reverse the
inequality symbol.
1
d > –2 4
Simplify.
Quick Check
Objective - To graph linear inequalities in the
coordinate plane.
Graph x  3.
Number Line
x3
-4 -3 -2 -1 0 1 2 3 4
Coordinate Plane
x3
y
x
x=3
Graph y  2.
Number Line
y  2
-4 -3 -2 -1 0 1 2 3 4
Coordinate Plane
y  2
y
x
y = -2
y
2
Graph y  x  1.
3
Boundary Line
2
y  x 1
3
2
m
b  1
3
x
Test a Point
2
y  x 1
3
2
0  (0)  1
3
0  1 False!
If y = mx + b,
solid dashed
shade up
shade down




Graph y   x  3.
Boundary Line
y
y  x  3

1
1
m  1 

1 1
b3
If y = mx + b,

Dashed line
Shade up
x
Graph 4x  5y  10.
4x  5y  10
4x
 4x
5y  4x  10
5
5

4
y
x2
5

4
4
m

5
5
b2
If y = mx + b,

Solid line
Shade up
y
x
Graph 3x  2y  8.
3x  2y  8
3x
 3x
2y  3x  8
2
2
3
y x4
2
3

3
m 
2 2
b  4
If y = mx + b,

Dashed line
Shade down
y
x
Point-Slope Equation
If you are given a point and a slope, you write the equation
of the line in point slope form by plugging in the slope and
the x and y from the point into:
y – y1 = m (x – x1)
y1 is the y from the point.
m is the slope.
x1 is the x from the point.
If you are asked to write the equation in slopeintercept form, first write the equation in pointslope form.
y – y1 = m (x – x1)
y1 is the y from the point.
m is the slope.
x1 is the x from the point.
Then distribute the “m” to the x and the x1
Then get the y alone on the left.
First write the equation in point- slope form.
y – y1 = m (x – x1)
m = ¼
(3,-2)
y1 is the y from the point.
m is the slope.
x1 is the x from the point.
y – -2 = ¼(x – 3)
Then distribute the “m” to the x and the x1
y – -2 = ¼x – ¾
Then get the y alone on the left.
y = ¼x – ¾ -2
y = ¼x –2¾
If you are given two points and no slope, you find the
slope using the slope formula:
y2 – y1
x2 – x1
Then write the equation of the line in point slope form by
plugging in the slope and the x and y from either one of
the points into:
y – y1 = m (x – x1)
y1 is the y from the point.
m is the slope.
x1 is the x from the point.