Solving Inequalities

Objective 3.2 The student will be able to: graph inequalities on a number line. solve inequalities using addition and subtraction.

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

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

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

4) Which inequality would have a closed dot on the number line? > < ≥ ≠ Answer Now

5) Which inequality does NOT use an open dot on the number line? ≤ < > ≠ Answer Now

o x - 14 < 16 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16 6) Solve x + (-14) < 16 x - 14 < 16 + 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

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

- 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 o 8) Solve 8y + 3 > 9y - 14 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 8(17) + 3 = 9(17) - 14 Draw “the river” Subtract 8y from both sides Simplify Add 14 to both sides Rewrite inequality with the variable first Check your answer Graph the solution o 17 18 16

● ● o o 9) What is the graph of 7 ≤ m? 7 8 6 7 8 6 7 8 6 7 8 6 Answer Now

- 2r - 2r r – 17 ≥ 14 + 17 + 17 r ≥ 31 10) Solve 3r - 17 ≥ 2r+14 ● + 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

11) Solve -2x + 6 ≥ 3x - 4 X ≥ -2 X ≤ -2 X ≥ 2 X ≤ 2 Answer Now

12) Joanna’s tests were 87, 93, 88 and 94 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? 96 97 98 100 Answer Now

Objective 3.3 The student will be able to: solve inequalities using multiplication and division.

1) Which graph represents the correct answer to > 1 -4 -3 -5 o -4 -3 -5 ● -4 -3 -5 ● -4 -3 -5 Answer Now

k < -52 o 1) Solve > 13 -52 -51 -53 Draw “the river” Clear the fraction - Multiply both sides by -4 NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! Simplify Check your answer Graph the solution k < -52 o -52 -51 -53

2) When solving > -10 will the inequality switch? Yes! No! I still don’t know! Answer Now

2) Solve < -10 x < -30 o -30 -29 -31 Draw “the river” Clear the fraction - Multiply both sides by 3. Do you switch the inequality? No - Both sides are being multiplied by a positive number Simplify Check your answer Graph the solution x < -30 o -30 -29 -31

3) When solving will the inequality switch? Yes! No! I still don’t know! Answer Now

a > -24 o 3) Solve -24 -23 -25 Draw “the river” Clear the fraction - Multiply both sides by -4. Do you switch the inequality? Yes - Both sides are being multiplied by a negative number Simplify Check your answer Graph the solution a > -24 o -24 -23 -25

Take a quick break! Things that make you go.....Hmmm Why is abbreviation such a long word? Why do they have braille dots on the ATM machines in drive-thru’s?

4) Solve -8p ≥ -96 p ≥ 12 p ≥ -12 p ≤ 12 p ≤ -12 Answer Now

p ≤ 12 -8(12) = -96 ● 4) Solve -8p ≥ -96 12 13 11 Draw “the river” Divide both sides by -8. Do you switch the inequality? Yes - Both sides are being divided by a negative number Simplify Check your answer Graph the solution p ≤ 12 -8(12) = -96 ● 12 13 11

● ● 5) Solve 7v < -105 o o -15 -14 -16 -15 -14 -16 -15 -14 -16 -15 Answer Now ● -15 -14