Question

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

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) $10\frac{1}{4}$

(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:

$\frac{3b}{3}$

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)