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Slide 1

1.6 Solving Inequalities

Slide 2

Solving inequalities follows the same procedures as solving equations.

There are a few special things to

consider with inequalities:

We need to look carefully at the inequality sign.

We also need to graph the solution set.

Slide 3

> greater than

< less than

greater than or equal

less than or equal

Slide 4

> Graph any number greater than. . .

open circle, line to the right

< Graph any number less than. . .

open circle, line to the left

Graph any number greater than or equal to. . .

closed circle, line to the right

Graph any number less than or equal to. . .

closed circle, line to the left

Slide 5

x + 4 < 7

-4 -4

x < 3

Subtract 4 from each side.

Keep the same inequality sign.

Graph the solution.

Open circle, line to the left.

Slide 6

Sometimes you may have to reverse the direction of the inequality sign!!

That only happens when you

multiply or divide both sides of the inequality by a negative number.

Slide 7

Example:

Solve: -3y + 5 >23

-5 -5

-3y > 18

-3 -3

y < -6

Subtract 5 from each side.

Divide each side by negative 3.

Reverse the inequality sign.

Graph the solution.

Open circle, line to the left.

Slide 8

Try these:

Solve 2x+3>x+5

Solve - c - 11>23

Solve 3(r-2)<2r+4

- Solving Inequalities
- Review of Inequality Signs
- How to graph the solutions
- Solve the inequality:
- There is one special case.

- Polynomials
- Real numbers
- Functions and Graphs
- Solve equations using addition and subtraction
- The Remainder and Factor Theorems
- Finding Reduced Basis for Lattices
- Solving Polynomial Equations

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