1. Solving multi-step equations and inequalities
Section 5.5

2. Objectives
Solve multi-step equations
Solve multi-step inequalities

3. Notes You can solve equations and inequalities with grouping symbols.
First, use the Distributive Property to remove the grouping symbols.

4. Examples
1. 3 = 4(x + 2)
2. 4(b - 3) < 72

5. EXAMPLES
3. Solve 4(x + 5) = 3(2x + 4)
4. 12m + 12 = 6(3m + 3)

6. Word pROBLEM
Mariella’s parents have budgeted $575 for her birthday party. The cost of the party room is $75. How much can the family spend per guest on food if each of the 40 guests receives a $5 favor? Write and solve an equation.

7. Solve Multi-step inequalities
Solve each inequality. Graph the solution on a number line.
5. -2(k + 1) > k
6. 2p + 5 > 3(p - 6)

8. No Solution or all numbers as solutions
Some equations have no solution. When this occurs, the solution is the __________________, shown by the symbol 0 or ().
Other equations may have every number as their solution.
An equation that is true for every value of the variable is called an __________.

9. Examples
1. 3(y - 5) + 25 = 3y + 10
2. -5s – 14 = 2(2s + 3) – 9s

10. EXAMPLES
3. -2(3r + 4) = -5r – 8 – r
w = 4(8 + 2w)

11. H.O.T. Problems
1. Write a multi-step inequality that can be solved by first adding 3 to each side.
2. Explain how you can solve45> -6x + 3 without multiplying or dividing by a negative number.