SOLVING MULTISTEP EQUATIONS AND INEQUALITIES SECTION 5 5

SOLVING MULTI-STEP EQUATIONS AND INEQUALITIES SECTION 5. 5

OBJECTIVES • Solve multi-step equations • Solve multi-step inequalities

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

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

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

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.

SOLVE MULTI-STEP INEQUALITIES • Solve each inequality. Graph the solution on a number line. • 5. -2(k + 1) > -16+ 5 k • 6. 2 p + 5 > 3(p - 6)

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 _____.

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

EXAMPLES • 3. -2(3 r + 4) = -5 r – 8 – r • 4. 14 + 8 w = 4(8 + 2 w)

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 solve 45> -6 x + 3 without multiplying or dividing by a negative number.