Linear Inequalities

By

Dr. Carol A. Marinas

Solving Linear Equations

• Linear Equations have no exponents higher than 1 and has an EQUAL SIGN.

• To solve linear equations1. 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

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

Examples• 2x + 4 < 6• 2x < 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.

Summary

Remember:

Use the same steps as Solving Linear Equations EXCEPT when Multiplying OR Dividing by a negative number you switch the inequality sign.