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
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
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) \( 10\frac{1}{4} \)
(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:
\( \frac{3b}{3} <\frac{39}{3} \)
b < 13 (Option A)
(4) The given expression:
4m + 9 + 5m – 12 = 42
9m = 42 + 12 - 9
9m = 45
Divide both sides with 9:
\( \frac{9m}{9} =\frac{45}{9} \\ m=5 \)
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:
\( \frac{12p}{12} >\frac{132}{12} \)
p > 11 (Option A)
(8) The given equation:
7x = 42
Divide the equation with 7 on both sides:
\( \frac{7x}{7} =\frac{42}{7} \)
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:
\( \frac{D}{AB} =\frac{ABC}{AB} \\ C =\frac{D}{AB} \)
Hence C = D ÷ AB (Option B)
(11) Given equation:
\( \frac{y}{9} + 5 = 0 \)
Subtract 5 on both sides:
\( \frac{y}{9} +5 -5 = 0 -5 \)
y = -5*9 = -45
y = -45 (Option B)
(12) Given equation:
12y = 132
Divide both sides by 12:
\( \frac{12y}{12} =\frac{132}{12} \)
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:
\( \frac{K}{LN} =\frac{LMN}{LN} \\ M = \frac{K}{LN} \)
Hence the correct answer is \( M = \frac{K}{LN} \) (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:
\( \frac{16y}{16} =\frac{164}{16} \\ y = 10\frac{1}{4} \)
Hence the correct answer is (Option C) \( y = 10\frac{1}{4} \)
(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)