## Chapter 4 Simple Equations Exercise 4.3

**Question 1: Solve the following equations:(a) 2y + (5/2) = (37/2)Answer:**

= 2y + 5/2 = 37/2

= 2y = 37/2 - 5/2

= 2y = 32/2

= y = 32/2 ÷ 2

= y = 8

**(b) 5t + 28 = 10**

Answer:

Answer:

= 5t + 28 = 10

= 5t = 10 - 28

= 5t = -18

= t= -18/5

= t = -18/5

**(c) (a/5) + 3 = 2**

Answer:

Answer:

= a/5 + 3 = 2

= a/5 = 2 - 3

= a/5 = -1

= a = -1 × 5

= a = -5

**(d) (q/4) + 7 = 5**

Answer:

Answer:

= q/4 + 7 = 5

= q/4 = 5 - 7

= q/4 = -2

= q × 4= -2 × 4

= q = -8

**(e) (5/2) x = -5**

Answer:

Answer:

= 5/2 x = -5

= 5x/2 × 2 = -5 × 2

= 5x = -10

= x = -10/5

= x = -2

**(f) (5/2) x = 25/4**

Answer:

Answer:

= 5/2 x = 25/4

= 5x/2 × 2 = 25/4 × 2

= 5x = 25/2

= x = 25/2 ÷ 5

= x = 25/2 × 1/5

= x = 5/2

(g) 7m + (19/2) = 13

Answer:

(g) 7m + (19/2) = 13

Answer:

= 7m + 19/2 = 13

= 7m = 13 - 19/2

= 7m = 7/2

= m = 7/2 ÷ 7

= m = 7/2 × 1/7

= m = 1/2

**(h) 6z + 10 = – 2**

Answer:

Answer:

= 6z + 10 = -2

= 6z = -2 - 10

= 6z = -12

= z = -12/6

= z = -2

**(i) (3/2) l = 2/3**

Answer:

Answer:

= 3/2 l = 2/3

= 3l/2 × 2 = 2/3 × 2

= 3l = 4/3

= l = 4/3 ÷ 3

= l = 4/3 × 1/3

= l = 4/9

**(j) (2b/3) – 5 = 3**

Answer:

Answer:

= 2b/3 = 3 + 5

= 2b/3 = 8

= 2b/3 × 3 = 8 × 3

= 2b = 24

= b = 24/2

= b = 12

Question 2: Solve the following equations:

(a) 2(x + 4) = 12

Answer:

Question 2: Solve the following equations:

(a) 2(x + 4) = 12

Answer:

= 2(x + 4) = 12

= 2x + 8 = 12

= 2x = 12 - 8

= 2x = 4

= x = 4/2

= x = 2

**(b) 3(n – 5) = 21**

Answer:

Answer:

= 3(n - 5) = 21

= 3n - 15 = 21

= 3n = 21 + 15

= 3n = 36

= n = 36/3

= n = 12

**(c) 3(n – 5) = – 21**

Answer:

Answer:

= 3(n - 5) = -21

= 3n - 15 = -21

= 3n = -21 + 15

= 3n = -6

= n = -6/3

= n = -2

**(d) – 4(2 + x) = 8**

Answer:

Answer:

= -4(2 + x) = 8

= -8 + -4x = 8

= -4x = 8 + 8

= -4x = 16

= x = 16/-4

= x = -4

**(e) 4(2 – x) = 8**

Answer:

Answer:

= 4(2 - x) = 8

= 8 - 4x = 8

= -4x = 8 - 8

= -4x = 0

= x = 0/-4

= x = 0

Question 3: Solve the following equations:

(a) 4 = 5(p – 2)

Answer:

Question 3: Solve the following equations:

(a) 4 = 5(p – 2)

Answer:

= 5(p - 2) = 4

= 5p - 10 = 4

= 5p = 4 + 10

= 5p = 14

= p = 14/5

= p = 14/5

(b) – 4 = 5(p – 2)

Answer:

(b) – 4 = 5(p – 2)

Answer:

= 5(p - 2) = -4

= 5p - 10 = -4

= 5p = -4 + 10

= 5p = 6

= 5p/5 = 6/5

= p = 6/5

**(c) 16 = 4 + 3(t + 2)**

Answer:

Answer:

= 4 + 3(t + 2) = 16

= 3(t + 2) = 16 - 4

= 3(t + 2) = 12

= 3t + 6 = 12

= 3t = 12 - 6

= 3t = 6

= t = 6/3

= t = 2

**(d) 4 + 5(p – 1) = 34**

Answer:

Answer:

= 4 + 5(p - 1) = 34

= 5(p - 1) = 34 - 4

= 5(p - 1) = 30

= 5p - 5 = 30

= 5p = 30 + 5

= 5p = 35

= p = 35/5

= p = 7

**(e) 0 = 16 + 4(m – 6)**

Answer:

Answer:

= 16 + 4(m - 6) = 0

= 4(m - 6) = 0 - 16

= 4(m - 6) = -16

= 4m - 24 = -16

= 4m = -16 + 24

= 4m = 8

= m = 8/4

= m = 2

Question 4: (a) Construct 3 equations starting with x = 2

Answer:

Question 4: (a) Construct 3 equations starting with x = 2

Answer:

= 10x + 2 = 22 (equation 1)

= 6x = 12 (equation 2)

= 5x - 3 = 7 (equation 3)

**(b) Construct 3 equations starting with x = – 2**

Answer:

Answer:

= 5x = -10 (equation 1)

= 5x - 3 = -13 (equation 2)

= 3x + 10 = 4 (equation 3)

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