Solved Examples on Algebra

Example 1: Solve the equation 5x – 6 = 3x – 8.

Solution:

Given,

5x – 6 = 3x – 8

Adding 6 on both sides,

5x – 6 + 6 = 3x – 8 + 6

5x = 3x – 2

Subtract 3x from both sides,

5x – 3x = 3x – 2 – 3x

2x = -2

Dividing both sides of the equation by 2,

2x/2 = -2/2

x = -1

Example 2:

�⁢�⁢�⁢�⁢�⁢�⁢�⁢�: 7⁢�+5�−4−6⁢�−1�−3−1�2−7⁢�+12=1

Solution:

Consider, x² – 7x + 12

= x² – 3x – 4x + 12

= x(x – 3) – 4(x – 3)

= (x – 4)(x – 3)

Now, from the given,7⁢�+5�−4−6⁢�−1�−3−1�2−7⁢�+12=1

Here, LCM of denominators = (x – 4)(x – 3)

Thus,

[(7x + 5)(x – 3) – (6x – 1)(x – 4) – 1]/ (x – 4)(x – 3) = 1

7x² – 21x + 5x – 15 – (6x² – 24x – x + 4) – 1 = (x – 4)(x – 3)

x² + 9x – 20 = x² – 7x + 12

9x + 7x = 12 + 20

16x = 32

x = 2