Download Linear Inequalities

Linear Inequalities
By
Dr. Carol A. Marinas
© Copyright 2010 Carol A. Marinas
Solving Linear Equations
•
•
Linear Equations have no
exponents higher than 1 and
has an EQUAL SIGN.
To solve linear equations
1. If fractions are involved, multiply
by the Least Common Multiples
of the denominators.
2. Simplify each side of the
equation
3. Move the terms so that the
variables are on one side and
the constants are on the other.
4. Divide by the coefficient of the
variable.
PROBLEM
x+2 + x = 3 + 1
x
4x x 4
1. Multiply by LCM (4, x, 4x) = 4x
4(x+2) + x = 12 + x
2. Simplify each side
4x + 8 + x = 12 + x
5x + 8 = 12 + x
3. Move terms
4x = 4
4. Divide by 4
x=1
© Copyright 2010 Carol A. Marinas
Solving Linear INequalities
• Use the same steps as Solving Linear
Equations EXCEPT when Multiplying OR
Dividing by a negative number you switch
the inequality sign.
WHY?
4 < 6 If you multiply both sides by –2
– 8 –12 In order for this to be true, it must be
flipped to a > sign.
– 8 > –12
© Copyright 2010 Carol A. Marinas
Examples
• 2x + 4 < 6
x<2
x<1
• This means that all
numbers less than
and including 1 will
make the original
inequality true.
• 3(1–x)+4>6
3 – 3x + 4 > 6
– 3x + 7 > 6
– 3x > – 1
x < 1/3
• Any number less than
1/3 will make the
original inequality true.
© Copyright 2010 Carol A. Marinas
Summary
Remember:
Use the same steps as Solving Linear
Equations EXCEPT when Multiplying OR
Dividing by a negative number you switch
the inequality sign.
© Copyright 2010 Carol A. Marinas