Bell Ringer 9/26/14 Test Questions

Objective 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 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

x < -30 2) Solve < -10 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

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

Objective The student will be able to: solve two-step inequalities.

1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 5(4) – 8 = 12 Draw “the river” Add 8 to both sides Simplify Divide both sides by 5 Check your answer Graph the solution o 4 5 3

- 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 o 2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18 Draw “the river” Subtract 12 from both sides Simplify Divide both sides by -3 Simplify (Switch the inequality!) Check your answer Graph the solution o -2 -1 -3

Which graph shows the solution to 2x - 10 ≥ 4? . Answer Now

o -2m -2m 3m - 4 < 11 + 4 + 4 3m < 15 3 3 m < 5 3) Solve 5m - 4 < 2m + 11 -2m -2m 3m - 4 < 11 + 4 + 4 3m < 15 3 3 m < 5 5(5) – 4 = 2(5) + 11 Draw “the river” Subtract 2m from both sides Simplify Add 4 to both sides Divide both sides by 3 Check your answer Graph the solution o 5 6 4

● -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 4) Solve 2r - 18 ≤ 5r + 3 -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 2(-7) – 18 = 5(-7) + 3 Draw “the river” Subtract 2r from both sides Simplify Subtract 3 from both sides Divide both sides by 3 Check your answer Graph the solution ● -7 -6 -8

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

5) Solve 26p - 20 > 14p + 64 o -14p -14p 12p – 20 > 64 + 20 + 20 + 20 + 20 12p > 84 12 12 p > 7 26(7) – 20 = 14(7) + 64 Draw “the river” Subtract 14p from both sides Simplify Add 20 to both sides Divide both sides by 12 Check your answer Graph the solution o 7 8 6

What are the values of x if 3(x + 4) - 5(x - 1) < 5? Answer Now

Objectives The student will be able to: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities.

● ● ● 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 o o b) Graph x ≥ 2 3 4 2 o 3 4 2 o b) Graph x ≥ 2 3 4 2 ● ● c) Combine the graphs d) Where do they intersect? ● 3 4 2 o

● ● 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 o o b) Graph x ≥ 4 3 4 2 o 3 4 2 o b) Graph x ≥ 4 3 4 2 ● 3 4 2 ● c) Combine the graphs

3) Which inequalities describe the following graph? -2 -1 -3 o y > -3 or y < -1 y > -3 and y < -1 y ≤ -3 or y ≥ -1 y ≥ -3 and y ≤ -1 Answer Now

4) Graph the compound inequality 6 < m < 8 When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8! 7 8 6 o

5) Which is equivalent to -3 < y < 5? y > -3 or y < 5 y > -3 and y < 5 y < -3 or y > 5 y < -3 and y > 5 Answer Now

6) Which is equivalent to x > -5 and x ≤ 1? Answer Now

● ● 7) 2x < -6 and 3x ≥ 12 o o o o -3 -6 -3 -6 4 7 1 4 7 1 Solve each inequality for x Graph each inequality Combine the graphs Where do they intersect? They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 -6 o -3 -6 o 4 7 1 o ● 4 7 1 o ●

Remember, when written like this, it is an AND problem! 8) Graph 3 < 2m – 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m – 1 AND 2m – 1 < 9 Solve each inequality. Graph the intersection of 2 < m and m < 5. 5 -

9) Graph x < 2 or x ≥ 4 5 -

The whole line is shaded!! 10) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!!