Archive
5th of April 2017
Mathematics
Q:

how to solve the problems of linear equation?

Ajay G. Gaddapod - CBSE - Class VII

Tuesday, April 04, 2017 at 19:24:PM

A:

Steps to solve a linear equation:


● Transfer all the x terms (that is all variable terms) on one side, and keep the numbers

   to the other side.

● Simplify each side and solve for x.

● Verify to be sure whether the answers satisfy the original equations.

Example: 

Solve the equation 6(3x + 2) + 5(7x - 6) - 12x = 5(6x - 1) + 6(x - 3) and verify your answer 

Solution: 

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

⇒ 18x + 12 + 35x - 30 - 12x = 30x - 5 + 6x - 18

⇒ 18x + 35x - 12x + 12 - 30 = 30x + 6x - 5 - 18 

⇒ 41x - 18 = 36x - 23

⇒ 41x - 36x = - 23 + 18 

⇒ 5x = -5

⇒ x = -1 

Therefore, x = -1 is the solution of the given equation. 

Verification: 

L.H.S. = 6(3x + 2) + 5(7x - 6) - 12x

Substitute the value of x = -1 we get; 

= 6[3 × (-1) + 2] + 5 [7 × (-1) - 6] - 12 × (-1) 

= 6[-3 + 2] + 5[-7 - 6] + 12

= 6 × (-1) + 5 (-13) + 12

= - 6 - 65 + 12

= -71 + 12

= -59

Verification: 

R.H.S. = 5(6x - 1) + 6(x - 3) 

Substitute the value of x = - 1, we get

= 5[6 × (-1) - 1] + 6[(-1) - 3] 

= 5(-6 - 1) + 6(-1 -3) 

= 5 × (-7) + 6 × (-4) 

= - 35 - 24 

= - 59

Since, L.H.S. = R.H.S. hence verified. 

Wednesday, April 05, 2017 at 09:44:AM