## Chapter 4 Simple Equations Exercise 4.3

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

= 2y + 5/2 = 37/2
= 2y = 37/2 - 5/2
= 2y = 32/2
= y = 32/2 ÷ 2
= y = 8

(b) 5t + 28 = 10

= 5t + 28 = 10
= 5t = 10 - 28
= 5t = -18
= t= -18/5
= t = -18/5

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

= a/5 + 3 = 2
= a/5 = 2 - 3
= a/5 = -1
= a = -1 × 5
= a = -5

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

= q/4 + 7 = 5
= q/4 = 5 - 7
= q/4 = -2
= q × 4= -2 × 4
= q = -8

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

= 5/2 x = -5
= 5x/2 × 2 = -5 × 2
= 5x = -10
= x = -10/5
= x = -2

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

= 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

= 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

= 6z + 10 = -2
= 6z = -2 - 10
= 6z = -12
= z = -12/6
= z = -2

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

= 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

= 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

= 2(x + 4) = 12
= 2x + 8 = 12
= 2x = 12 - 8
= 2x = 4
= x = 4/2
= x = 2

(b) 3(n – 5) = 21

= 3(n - 5) = 21
= 3n - 15 = 21
= 3n = 21 + 15
= 3n = 36
= n = 36/3
= n = 12

(c) 3(n – 5) = – 21

= 3(n - 5) = -21
= 3n - 15 = -21
= 3n = -21 + 15
= 3n = -6
= n = -6/3
= n = -2

(d) – 4(2 + x) = 8

= -4(2 + x) = 8
= -8 + -4x = 8
= -4x = 8 + 8
= -4x = 16
= x = 16/-4
= x = -4

(e) 4(2 – x) = 8

= 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)

= 5(p - 2) = 4
= 5p - 10 = 4
= 5p = 4 + 10
= 5p = 14
= p = 14/5
= p = 14/5

(b) – 4 = 5(p – 2)

= 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)

= 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

= 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)

= 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

= 10x + 2 = 22 (equation 1)
= 6x = 12 (equation 2)
= 5x - 3 = 7 (equation 3)

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