Question

1. Solve this problem: –282 – (+1,017) = ? A. 735

B. –1,299
C. –735
D. 1,299
2. Sue has a balance of $35 in her checking account. She writes one check for $10, and three checks for $9 each. What is her balance now?
A. –$2 B. $54 C. –$11 D. $18
3. Solve this inequality: 3b – 7 < 32 A. b < 13
B. b < 5
C. b < 39
D. b < 8.33
4. Simplify and solve this equation: 4m + 9 + 5m – 12 = 42. A. m = –5
B. m = 4
C. m = -4
D. m = 5
5. Simplify this expression: 13 + (–12) – (–5) = ? A. 30
B. –30
C. –6
D. 6
6. If four times a number plus 3 is 11, what is the number?
A. 5 B. 2 C. 4 D. 16
7. Solve the inequality: 12p + 7 > 139 A. p > 11
B. p > 154
C. p > 18
D. p > 12
8. Solve the equation: 7x = 42. A. x = 7
B. x = 6
C. x = – 7
D. x = – 6
9. Solve this inequality: 9h + 2 < –79. A. h < – 9
B. h < –10
C. h < 10
D. h < 9
10. Given the formula D = ABC, what is the formula for C? A. C = AB ÷ D
B. C = D ÷ AB
C. C = AD ÷ C
D. C = ABD
11. Solve this equation: y/9 + 5 = 0.
A. y = –5 B. y = –45 C. y = 45 D. y = 5
12. Solve the equation: 12y = 132. A. y = 11
B. y = 11/12 C. y = 144 D. y = 1/11
13. Simplify and solve this equation for q: 3q + 5 + 2q – 5 = 65. A. q = 23
B. q = 11
C. q = 15
D. q = 13
14. Given the formula K = LMN, what is the formula for M? A. M = K/LN
B. M = LN/K C. M = KL/N
D. M = LNK
15. Solve the equation: h/9 = 7. A. h = 1 2/7
B. h = –63 C. h = 63
D. h = 7/9
16. Simplify this expression: 4p + 9 + (–7p) + 2 = ? A. 11p + 11
B. 3p + 11
C. –3p + 11
D. 3p + 7
17. Find the value of y in this equation: 16y = 164. A. 32
B. 180
C. 10 1/4
D. 16 1/4
18. Solve this equation: 4y + 228 = 352. A. y = 145
B. y = – 31
C. y = 3
D. y = 31
19. Given the formula E = IR what is the formula for R? A. R = I ÷ E
B. R = IE
C. R = EI D. R = E ÷ I
20. Solve the following equation: 6y – 20 = 2y – 4. A. y = 3
B. y = 4
C. y = 16
D. y = 2

Answer 1

1. -282 -(1017) = -282 - 1017 = - 1299
2. 35 - (10 + 3(9)) = 35 - (10 + 27) = 35 - 37 = -2
3. 3b - 7 < 32....3b < 32 + 7.....3b < 39.....b < 39/3....b < 13
4. 4m + 9 + 5m - 12 = 42....9m - 3 = 42...9m = 42 + 3.....9m = 45.....m = 45/9...m = 5
5. 3 + (-12) - (-5) = 3 - 12 + 5 = 8 - 12 = -4
6. 4 times a number plus 3 is 11.......4x + 3 = 11...4x = 11 - 3....4x = 8...x = 8/4....x = 2
7. 12p + 7 > 139...12p > 139 - 7.....12p > 132....p > 132/12....p > 11
8. 7x = 42...x = 42/7....x = 6
9. 9h + 2 < -79....9h < -79 - 2...9h < -81....h < -81/9...h < - 9
10. D = ABC.....C = D/AB
11. y/9 + 5 = 0...y/9 = -5....y = -5*9...y = -45
12. 12y = 132....y = 132/12...y = 11
13. 3q + 5 + 2q - 5 = 65....5q = 65....q = 65/5....q = 13
14. K = LMN....M = K/LN
15. h/9 = 7.....h = 7*9...h = 63
16. 4p + 9 + (-7p) + 2 = 4p + 9 - 7p + 2 = -3p + 11
17. 16y = 164...y = 164/16...y = 10.25 or 10 1/4
18. 4y + 228 = 352...4y = 352 - 228...4y = 124....y = 124/4...y = 31
19. E = IR.....R = E/I
20. 6y - 20 = 2y - 4.....6y - 2y = -4 + 20....4y = 16...y = 16/4....y = 4

Answer 2

The correct answers are:

(1) (Option B) -1299

(2) (Option A) -2

(3) (Option A) b < 13

(4) (Option D) m = 5

(5) (Option D) 6

(6) (Option B) 2

(7) (Option A) p > 11

(8) (Option B) x = 6

(9) (Option A) h < –9

(10) (Option B) C = D ÷ AB

(11) (Option B) y = –45

(12) (Option A) y = 11

(13) (Option D) q = 13

(14) (Option A) M = K/LN

(15) (Option C) h = 63

(16) (Option C) –3p + 11

(17) (Option C)
`10(1)/(4)`

(18) (Option D) y = 31

(19) (Option D) R = E ÷ I

(20) (Option B) y = 4

Explanations:

(1) The Given Expression:

-282 - (+1017)

= -282 - 1017

= -1299 (Option B)

(2) The total balance = $35

One check = $10

Three checks = 3 * $9 = $27

Balance now = Total balance - One check + Three check = $35 - $10 - $27 = -2 (Option A)

(3) The given expression:

3b – 7 < 32

Add 7 on both sides:

3b -7 + 7 < 32 + 7

3b < 39

Divide by 3 on both sides:

`(3b)/(3) <(39)/(3)`

b < 13 (Option A)

(4) The given expression:

4m + 9 + 5m – 12 = 42

9m = 42 + 12 - 9

9m = 45

Divide both sides with 9:

`(9m)/(9) =(45)/(9) \\ m=5`

The correct answer is m=5 (Option D)

(5) The given expression:

13 + (–12) – (–5)

= 13 - 12 + 5

= 6 (Option D)

(6) Mathematically, we can write "four times a number plus 3 is 11" as:

4x + 3 = 11

Where,

x = The number we require

4x = 11 - 3

4x = 8

x = 2 (Option B)

(7) The given expression:

12p + 7 > 139

Subtract 7 on both sides:

12p + 7 - 7 > 139 -7

12p > 132

Divide 12 on both sides:

`(12p)/(12) >(132)/(12)`

p > 11 (Option A)

(8) The given equation:

7x = 42

Divide the equation with 7 on both sides:

`(7x)/(7) =(42)/(7)`

x = 6 (Option B)

(9) The given expression:

9h + 2 < –79

Subtract 2 on both sides:

9h + 2 - 2 < -79 - 2

9h < -81

h < -9 (Option A)

(10) The given equation:

D = ABC

Now divide both sides with AB on both sides:

`(D)/(AB) =(ABC)/(AB) \\ C =(D)/(AB)`

Hence C = D ÷ AB (Option B)

(11) Given equation:

`(y)/(9) + 5 = 0`

Subtract 5 on both sides:

`(y)/(9) +5 -5 = 0 -5`

y = -5*9 = -45

y = -45 (Option B)

(12) Given equation:

12y = 132

Divide both sides by 12:

`(12y)/(12) =(132)/(12)`

y = 11 (Option A)

(13) The given equation:

3q + 5 + 2q – 5 = 65

5q = 65

Divide both sides with 5 and simplify:

q = 13 (Option D)

(14) Given formula:

K = LMN

To find M, divide both sides with LN:

`(K)/(LN) =(LMN)/(LN) \\ M = (K)/(LN)`

Hence the correct answer is
`M = (K)/(LN)` (Option A)

(15) Given formula:

h/9 = 7

Multiply both sides with 9:

h = 7 * 9

h = 63 (Option C)

(16) Given expression:

4p + 9 + (-7p) + 2

4p + 9 -7p +2

-3p + 11 (Option C)

(17) The given formula:

16y = 164

Divide both sides with 16:

`(16y)/(16) =(164)/(16) \\ y = 10(1)/(4)`

Hence the correct answer is (Option C)
`y = 10(1)/(4)`

(18) Given equation:

4y + 228 = 352

Subtract both sides with 228:

4y + 228 - 228 = 352 - 228

4y = 124

Divide both sides by 4 and simplify:

y = 31 (Option D)

(19) The given formula:

E = IR

To find R, divide both sides with I:

R = E ÷ I (Option D)

(20) Given equation:

6y - 20 = 2y - 4

=> 6y - 2y = -4 + 20

=> 4y = 16

Divide both sides with 4 and simplify:

y = 4 (Option B)