4-7 & 4-8 Solving Inequalities by Adding & Subtracting Objective The student will be able to: graph inequalities on a number line. 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 2x = 5 Not solved -3x =6 Not solved

greater than or equal to 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 When you have < or >, use an open dot!

Graph the solution set of y ≥ -5/4 • When you have ≤ or ≥, use a closed dot! Convert -5/4 to a decimal = -1.25

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

What is the graph of 7 ≤ m? o 7 8 6 o 7 8 6 ● 7 8 6 ● 7 8 6 Answer Now

What type of dot open or closed? < > ≤ ≥ ≠ Open Open Closed 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. x - 14 < 16 y + 21 ≥ 7 x – 14 + 14 < 16 +14 y + 21 - 21 ≥ 7 - 21

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

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

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

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

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

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

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