Radicals and Inequalities Practice Quiz Radicals and Inequalities

7 + 4 11 Find x + 4 when x = 7 4x – 3 = 25 +3 +3 4x = 28 x = 7 If , then find the value of x + 4 ? 1 Find x + 4 when x = 7 7 + 4 4x – 3 = 25 +3 +3 11 4x = 28 x = 7

If , then x – 5 equals 2 Find x – 5 when x = 18 –7 –7 18 – 5 13 2x = 36 x = 18

49 < x – 2 < 64 51 < x < 66 +2 +2 +2 If x is an integer and , how many different values of x are possible? 3 First, solve inequality. 49 < x – 2 < 64 +2 +2 +2 51 < x < 66

51 < x < 66 If x is an integer and , how 3 many different values of x are possible? 3 51 < x < 66 Integers between 51 and 66 OR 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 – 51 = 15 15 – 1 = 14 Answer: 14 Values

3 Try this strategy How many values of m are possible? Use an inequality with two numbers that are close together. 2 < m < 7 Integers between 2 and 7 3 4 5 6 How many values of m are possible? 10 < m < 45 Answer: 4 Values OR 45 – 10 = 35 35 – 1 = 34 7 – 2 = 5 5 – 1 = 4

9 < m + 1 < 25 8 < m < 24 –1 –1 –1 If m is an integer and , how many different values of m are possible? 4 First, solve inequality. 9 < m + 1 < 25 –1 –1 –1 8 < m < 24

8 < m < 24 If m is an integer and , how 4 many different values of m are possible? 4 8 < m < 24 Integers between 8 and 24 OR 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 – 8 = 16 16 – 1 = 15 Answer: 15 Values

5 5x + 3 = 3x + 7 –3x –3x 2x + 3 = 7 –3 –3 2x = 4 x = 2

6 The equation has ___ solution(s). (x + 5)2 (x + 5)(x + 5) x2 + 5x + 5x + 25 2x + 13 = x2 + 10x + 25 x2 + 10x + 25 –2x – 13 –2x – 13 0 = x2 + 8x + 12 12 0 = (x + 2)(x + 6) 2 6 x + 2 = 0 , x + 6 = 0 8 x = –2 , x = –6

3 = 3 1  –1 6 x = –2 x = –6 The equation has ___ solution(s). YES NO Check Answers x = –2 x = –6 3 = 3 1  –1 One negative solution YES NO

x – 2 = x2 – 4x + 4 –x + 2 –x + 2 0 = x2 – 5x + 6 0 = (x – 2)(x – 3) 7 The equation has ___ solution(s). (2 – x)2 (2 – x)(2 – x) 4 – 2x – 2x + x2 x – 2 = x2 – 4x + 4 x2 – 4x + 4 –x + 2 –x + 2 0 = x2 – 5x + 6 6 0 = (x – 2)(x – 3) –2 –3 x – 2 = 0 , x – 3 = 0 –5 x = 2 , x = 3

0 = 0 1  –1 7 x = 2 x = 3 The equation has ___ solution(s). YES NO Check Answers x = 2 x = 3 0 = 0 1  –1 YES NO One positive solution

8 –25 –25 w = 256

If and , then what is the value of b ? 9 a = 64 b = 16

y Step 1 Step 2 Step 3 y = 16 x = 9 10 If and , then what is the value of x ? 10 Step 1 Step 2 Step 3 y y = 16 x = 9

11 0 > 5x – 1 +1 +1 1 > 5x

12 –3x + 13 < –14 –13 –13 –3x < –27 x > 9

13 7x – 3 > 4x – 5 –4x –4x 3x – 3 > –5 +3 +3 3x > –2

14 2x = 1 NO NO If , then which of the following statements must be true? 14 Strategy: Substitute ¼ for x in each answer. 2x = 1 NO NO

14 2x > 1 NO NO If , then which of the following statements must be true? 14 Strategy: Substitute ¼ for x in each answer. 2x > 1 NO NO

15 2x = –1 YES NO NO If –1 < x < 0 , then which of the following statements must be true? 15 Strategy: Substitute –½ for x in each answer. 2x = –1 YES NO NO

15 2x > 1 NO YES If –1 < x < 0 , then which of the following statements must be true? 15 Strategy: Substitute –½ for x in each answer. 2x > 1 NO YES

If –1 < x < 0 , then which of the following statements must be true? 15 Strategy: Substitute –⅛ for x in each answer. A. 2x = –1 is not correct NO

If , then which of the following inequalities is correct? 16 m = 0.5 m3 = 0.125 m3 < m2 < m

If , then which of the following inequalities is correct? 17 K = –0.333 K3 = –0.037 K < K3 < K2

10 < x x 10 < x x –10 10 < –10 –5 10 < –5 –1 < –10 If , then which of the following values could be x ? 18 Strategy: Test each answer by substituting for x. A. –10 B. –5 10 < x x 10 < x x –10 10 < –10 –5 10 < –5 –1 < –10 –2 < –5 NO NO

10 < x x 10 < x x 10 < x x 1 10 < 1 2 10 < 2 5 10 If , then which of the following values could be x ? 18 C. 1 D. 2 E. 5 10 < x x 10 < x x 10 < x x 1 10 < 1 2 10 < 2 5 10 < 5 10 < 1 5 < 2 2 < 5 NO NO YES

½ > 3 x > x 6 x > x 6 6 > 6 6 3 > 3 1 > 6 A. 6 B. 3 If , then which of the following values could be x ? 19 Strategy: Test each answer by substituting for x. A. 6 B. 3 x > x 6 x > x 6 6 > 6 6 3 > 3 1 > 6 NO ½ > 3 NO

–½ > –3 x > x 6 x > x 6 6 > 0 6 –3 > –3 0 > 0 C. 0 If , then which of the following values could be x ? 19 C. 0 D. –3 E. x > x 6 x > x 6 Cannot be determined 6 > 0 6 –3 > –3 0 > 0 –½ > –3 NO YES

z < 0 20  y = ( + ) positive y > 0 x > y  If x > y and y > 0 and xz < 0, then which of the following must be true about all the values of z? 20  y = ( + ) positive y > 0 x > y  x = ( + ) positive xz < 0  xz = ( – ) negative (+)z = ( – ) z < 0 (+)(–) = ( – ) z is negative

x = y m > y m > x x < m 21 If x = y and m > y, then which of the following must be true? 21 I. x < m II. x = m III. x > m x = y (Given) m > y m > x (Given) Equivalent to x < m

22 xy < 0  xy = negative answer   x > y x is positive + If x > y and xy < 0, which of the following inequalities must be true? 22 I. x > 0 II. y > 0 III. xy < 0  xy = negative answer One number is positive One number is negative   x > y x is positive + y is negative –

22  x is positive + x > y y is negative – If x > y and xy < 0, which of the following inequalities must be true? 22 I. x > 0 II. y > 0 III.  x > y x is positive + y is negative –

x – 7 = 0 x – 1 = 0 x = 7 x = 1 1 7 (0 – 7)(0 – 1) > 0 What are all the values of x for which (x – 7)(x – 1) > 0 ? 23 x – 7 = 0 x – 1 = 0 x = 7 x = 1 A B C YES NO YES 1 7 Test Section A with x = 0 (0 – 7)(0 – 1) > 0 (–7)(–1) > 0 x < 1 or x > 7 7 > 0 YES

x + 6 = 0 x + 3 = 0 x = –6 x = –3 –6 –3 (0 + 6)(0 + 3) < 0 What are all the values of x for which (x + 6)(x + 3) <0 ? 24 x + 6 = 0 x + 3 = 0 x = –6 x = –3 A B C NO YES NO –6 –3 Test Section C with x = 0 (0 + 6)(0 + 3) < 0 (6)(3) < 0 –6 < x < –3 18 < 0 NO

x + 2 = 0 x – 5 = 0 x = –2 x = 5 –2 5 (0 + 2)(0 – 5) > 0 What are all the values of x for which (x + 2)(x – 5) > 0 ? 25 x + 2 = 0 x – 5 = 0 x = –2 x = 5 A B C YES NO YES –2 5 Test Section B with x = 0 (0 + 2)(0 – 5) > 0 (2)(–5) > 0 x < –2 or x > 5 –10 > 0 NO