Page 48 - Concepts of Reasoning-8

CHAPTER

Worksheet-8.1 linear equations 8

Solving Equations by Reducing them to Linear Forms

1. Match the following :

Group A Group B
a. 5x + 17 (2 + 2x) = 16 (1 + 4x) ( ) i. 3x – 4 = 2x + 16
3 x
b. x – 1 = + 4 ( ) ii. 12x + 5 = 6x + 7
4 2
c. 8x – 5 3 ( ) iii. 39x + 34 = 16 + 64x
=
7x – 1 –6
3x – 2 2x + 3 7
d. + = x + ( ) iv. –11x + 55 = 38x + 34
3 2 6
e. 3x + 1 2x – 3 = x +3 + 3x – 1 ( ) v. 16x – 10 = 1 – 7x
–
16 7 8 14
2. State whether the following statements are true or false :
x 3 1 x 1 3
+
= 1 –
–
=
a. , solution; x = 9 b. , solution; x = 5
7 7 7 5 2 2
5 4y + 3
c. 3y + 2 = 7, solution; y = d. = 5, solution; y = –3
2 5
3. The following equations have been solved, but the steps given are not in the correct sequence. What
should be the correct sequence? Write the numbers in the correct order, separated by commas.
x 1 x
a. + 5 = + 6
2 2 3
x 1 x x 1 3x – 2x 1
i. = ii. – = 6 – 5 iii. x = 3 iv. =
6 2 2 3 2 6 2
Correct sequence : __________
b. 0.8x + 1.25 = 2x + 0.05

i. –120x = –120 ii. 80x + 125 = 200x + 5 iii. 8 x + 125 = 2x + 5
10 100 100
iv. 80x – 200x = –125 + 5 v. x = 1 vi. 80x + 125 = 200x + 5
100 100
Correct sequence : __________
x 2x 2x 11
c. – = –
3 5 3 30
–11x 11 5x – 6x – 10x 11 –1
i. = ii. – iii. x =
15 30 15 30 2
x 2x 2x 11 11 15
iv. – – = v. x = ×
3 5 3 30 30 –11
Correct sequence : __________

48 Reasoning - 8