1. Solving Equations and Inequalities
Chapter 7

2. Solving Two-Step Equations continued…
   
Do the inverse operation for
addition or subtraction first.
Do the inverse operation of
multiplication or division last.

3. Steps for Solving a Multi-Step Equation
Step 1: Use the Distributive Property, if necessary.
Step 2: Combine like terms.
Step 3: Undo addition or subtraction.
Step 4: Undo multiplication or division.
Let’s Practice

4. Solving Multi-Step Equations with Fractions
Examples
4x= n-6=22
-7k+14= x+3=2

5. Quick Check
Solve each equation:
-7 + y = b. 1b – 1 =
c. 1.5x – 3.6 = d p – 3 = 0.71

6. 1.6 Solving Inequalities

7. Solving Inequalities
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.

8. Review of Inequality Signs
Solving Inequalities
Review of Inequality Signs
> greater than
< less than
greater than or equal
less than or equal

9. How to graph the solutions
> 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

10. Solve the inequality: -4 -4 x < 3 x + 4 < 7
x < 3
Subtract 4 from each side.
Keep the same inequality sign.
Graph the solution.
Open circle, line to the left. 3

11. Example: -3y > 18 Solve: -3y + 5 >23 -5 -5
-3y > 18
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. -6

12. Try these:
Solve 2x+3>x+5
Solve - c - 11>23
Solve 3(r-2)<2r+4