Download Solving One-Step Inequalities

Solving One-Step
Inequalities
x  7  12
x  7  12
2
3 4 5 6
7
8
Solving One-Step
Inequalities
Objective: To solve
one-step inequalities using
properties for inequalities
Solving One-Step
Inequalities
What are the
Properties for Inequalities?
Are they the same as for
regular equations?
Solving One-Step Inequalities
Addition Property for Inequalities
x -15 < 73
Add 15 to
both sides
x -15 < 73
+ 15 + 15
x < 88
Solving One-Step Inequalities
Subtraction Property for Inequalities
y + 15 < 25
Subtract 15
from both sides
y +15 < 25
- 15
- 15
y < 10
Solving One-Step Inequalities
Multiplication Property for Inequalities
Multiply both
sides by the
reciprocal of
the coefficient
x
5   10  5
5
x
 10
5
x  50
Solving One-Step Inequalities
Division Property for Inequalities
Divide both
sides by the
coefficient
of x
5 x 20

5
5
5x  20
x4
Division Property for
Inequalities
Caution! Dividing by
 5x  20
 5 x 20

5 5
a negative number
Same if multiplying?
Notice: Sign
CHANGED
x  4
Multiplication Property for
Inequalities
YES
-x! > 2
5
(-5 )-x > 2(-5)
1
5
Caution! When you
multiply by a
negative number…
…the sign
CHANGES
x < -10
Solving One-Step
Inequalities
Let’s try some on
our own …… ready?
Solving One-Step
Inequalities
1
x6 7
Solving One-Step
Inequalities
2
3  x 5
Solving One-Step
Inequalities
3
 3x  15
Solving One-Step
Inequalities
4
x  9  5
Answers for #1 - #4
1. x ≤ 1
2. 8 ≤ x or x ≥ 8
3. x ≤ 5
4. x > 4
Solving One-Step
Inequalities
5
1
x  3
2
Solving One-Step
Inequalities
6
x
3 
7
Solving One-Step
Inequalities
7
5 x  7
Solving One-Step
Inequalities
8
x
5
3
Answers for #5 - #8
5. x ≥ -6
6. 21 < x or x > 21
7. x ≥ 2
8. x > 15