Linear Equations

Question 1

solve 2x + 3

Answer 1

x = 3

Question 2

2(y - 4) = 5y - 3

Answer 2

y = - 5/3 = -1 2/3

Question 3

5/2x + 3 1/2 = 2/3x + 5

Answer 3

x = 9/11

Question 4

(z + 2)/3 = (3z + 2)/5

Answer 4

z = 1

Question 5

9/(2x - 5) = 3

Answer 5

x = 4

Question 6

(y + 4)/(2y - 3) = 2/3

Answer 6

y = -26

Question 7

The sum of three consecutive events numbers is 60. Find the numbers

Answer 7

Let the smallest even number be n.
Then the other two consecutive even numbers will be n + 2 and n + 4.

∴ sum of the three consecutive events numbers numbers
= n + (n + 2) + (n + 4) = 60
n = 18

Question 8

Ali walked at an average speed of 3 km/h for 45 minutes before running for half an hour at a certain average speed. If he travelled a total distance of 6 km, calculate his average running speed.

Answer 8

Total distance walked = average walking speed x walking time
= 3 x 45/60
= 9/4 km
Let Ali’s average running speed be x km/h.
Total distance ran
= average running speed x running time
= x x 1/2
= x/2km

∴ total distance travelled = 9/4 + x/2

∴ 9/4 + x/2 = 6

9 + 2x = 24
2x = 15
x = 7.5

∴ Ali’s average running speed = 7.5km

Attention
Since the average running speed is x km/h, then x is a number without any unit.
= XX
2
=
- km
2
9
:: total distance travelled =
一十
4
2
..
9
4*
2 = 6
9 + 2x = 24
2x = 15
x = 7.5
. Ali’s average running speed = 7.5 km/h

Question 9

The formula for finding the volume V of a cuboid is given by V = Lbh, where L, b and h
represent the length, the breadth and the height of the cuboid respectively.
(a) If L = 5 cm, b = 2 cm and h = 3 cm, calculate the volume of the cuboid.
(b) If V = 240 cm³, b = 6 cm and h = 5 cm, calculate the length of the cuboid.

Answer 9

(a) 5x2x3 = 30cm³
(b) V = 240, b = 6, h = 5, L x 6 x 5 = 240
30 L = 240
L = 240/30 = 8cm
∴ length of cuboid = 8cm

Question 10

(i) Find a formula for the sum S of any three consecutive odd numbers. (ii) Hence, find the value of S if the greatest odd number is -101.

Answer 10

(i) Let the smallest odd number be n.
Then the other two consecutive odd numbers will be n + 2 and n + 4.
∴ sum of the three consecutive odd numbers,
S = n+ (n + 2) + (n+ 4)
= 3n + 6, where n is odd
(ii) If the greatest odd number is -101, then n + 4 = - 101
n = -101 - 4
= -105

∴ S = 3n + 6 = 3 x (-105) + 6 = -309