4 7 4 8 Solving Inequalities by Adding

4 -7 & 4 -8 Solving Inequalities by Adding & Subtracting Objective The student will be able to: 1. graph inequalities on a number line. 2. solve inequalities using addition and subtraction.

To solve for a variable the variable must be positive with no number beside it!! x = 10 Solved - x = -5 Not solved 2 x = 5 Not solved -3 x =6 Not solved

INEQUALITIES Another type of sentence used in algebra is called an inequality. An inequality is used when we don't know exactly what an expression is equal to. Instead of an equals sign, we use one of these symbols: This will be easier to do if you remember that the open part of the symbol always faces the larger quantity. SYMBOL MEANING < < less than > greater than ≤ ≥ less than or equal to greater than or equal to

Graph the solution set of x < 3 o When you have < or >, use an open dot! open dot

Graph the solution set of y ≥ -5/4 • When you have ≤ or ≥, use a closed dot! closed dot Convert -5/4 to a decimal = -1. 25

Graph the solution set of p ≠ 2 o When you have ≠, use an open dot and shade both ways!

What is the graph of 7 ≤ m? 1. 2. 3. 4. 6 6 o 7 8 o ● 7 Answer Now 8 8

What type of dot open or closed? 1. 2. 3. 4. 5. < > ≤ ≥ ≠ Open Closed Open

Pg 207 5 -10 odd • Do in class together – Will have for homework tonight these types of problems.

Addition & Subtraction property of inequality • You can add or subtract the same number or term on each side of the inequality, the relationship between the two sides does not change. y + 21 ≥ 7 x - 14 < 16 y + 21 - 21 ≥ 7 - 21 x – 14 + 14 < 16 +14

1) Solve x + (-14) < 16 Solve this problem like an equation 1. Draw “the river” 2. Eliminate double signs 3. Add 14 to both sides 4. Simplify 5. Check your answer 6. Graph the solution 29 x - 14 < 16 + 14 x < 30 30 + (-14) = 16 16 = 16 o 30 31

1. 2. 2) Solve y + 21 ≥ 7 - 21 -21 Draw the “river” Subtract 21 from y ≥ -14 both sides 3. Simplify 4. Check your answer 5. Graph the solution -15 21 + (-14) = 7 7 = 7 ● -14 -13

3) Solve y + 3 > - 14 1. 2. 3. 4. 5. Draw “the river” Subtract 3 from both sides Simplify Check your answer Graph the solution -18 - 3 y > -17 + 3 = - 14 o -17 -16

1. 2. 3. 4. 5. 6. 7. 4) Solve 3 r - 17 ≥ 2 r + 14 - 2 r Draw “the river” Subtract 2 r from both r – 17 ≥ 14 sides Simplify + 17 Add 17 to both sides Simplify r ≥ 31 Check your answer Graph the solution 30 3(31) - 17 = 2(31) + 14 ● 31 32

Solve and graph -2 x + 6 ≥ 3 x - 4 x ≤ 2

Joanna’s tests were 87, 93, 88 and 94. What must her 5 th grade be to get a total of at least 459? X + 87 + 93 + 88 + 94 ≥ 459 X + 362 ≥ 459 -362 X ≥ 97 ≥

Homework Day One Pg. 207 4 -28 even all one point each Homework Day Two Pg. 212 4 -10, 22 -36 even all two points a piece, (graphing and work)