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Warm-up: Solve for x.
1. 6x + 12 = -15 + 3x
2. 2x + 3(x – 5) = 25
3. 20 – 7x = -4(2x – 6)
4. 2x + 15 – 5x = 3(x – 7)
Determine whether the given number is a
solution of the inequality.
1. x + 3 < 6 ; 5
False, not a solution
8<6
2. 2x – 3 > -3 ; 1
2 – 3 > -3
-1 > -3
True, it is a solution
3. 4x – 1  3x + 2 ; 3 True, it is a solution
12 – 1  9 + 2
11  11
Graphing One
Variable
Inequalities
1. Distribute.
2. Combine like terms.
3. Move variable to the left side if needed
(add or subtract)
4. Get rid of constant (add or subtract)
5. Get rid of coefficient or denominator
(divide or multiply)
**Be careful – Dividing or Multiplying by a
Negative will switch your inequality sign**
Inequality Signs
When graphing the number use a …
Closed Circle OPEN Circle
<>
<>
Graph Using a Number Line
1.) Graph x < 2
2.) Graph x  - 3
2
Opened Circle
-3
Closed Circle
Shade to the left
Shade to the right
Solve, then graph.
3.
x+4>7
-4 -4
x>3
4.
3x  1   3
x  2
Try These:
Solve then graph.
5.
x
6   16
4
6.
5  2 x  11
Graphing
Linear
Inequalities
Checking Solutions
An ordered pair (x,y) is a solution if it makes the
inequality true.
Are the following solutions to:
3x + 2y ≥ 2
1. (0,0)
3(0) + 2(0) ≥ 2
0≥2
Not a solution
2. (2,-1)
3(2) + 2(-1) ≥ 2
4≥2
Is a solution
3. (0,1)
3(0) + 2(1) ≥ 2
2≥2
Is a solution
Write in Slope-Intercept Form
4. 2y < 8x + 10
5. 2x – y > -3
Solid or Dashed??
Solid or Dashed??
To sketch the graph of a linear inequality:
1. Sketch the line given by the equation
(solid if ≥ or ≤, dashed if < or >). This line
separates the coordinate plane into 2
halves.
o In one half-plane – all of the points are
solutions of the inequality.
o In the other half-plane - no point is a
solution
2. You can decide which half to shade by
testing ONE point.
3. Shade the half that has the solutions to the
inequality.
Graph the inequality
6. y ≥ -3/2x + 1
Graph the line
Before you connect the dots check to see if the line
should be solid or dashed
solid if ≥ or ≤
dashed if < or >
6. y ≥ -3/2x + 1
Step 1: Graph the
boundary
(the line is solid ≥)
Step 2: test a point NOT
on the line
(0,0) is always
the easiest if it’s
Not on the line!!
(0) ≥ -3/2(0) + 1
0≥1
Not a solution
So shade the other side of the line!!
7. Graph: y < 6
8. 4x – 2y < 6
9. 2x – 6y > 18