Page 62 - SM inner class 8.cdr

Solving a linear equation We can simplify this equation by
transpositioning further as:
As we have learnt how to use the four rules of
solving the Linear Equation with variable. 5x = 25
Lets see a detail example of solving the x = 25 [transpositioning of 5 and sign change
equation. 5
to ¸ from ´]
To do this we follow the steps below:
x = 5
Step 1. First simplify the equations on
both the sides so that they cannot Therefore, x = 5 is the solution of the given
be further simplified. equation.
1
Step 2. Now, bring all the variable terms Example 2: Solve the equation 10x = 3x + .
2
to one side of the equation (LHS is
mostly preferred) and numerals on Solution: 10x = 3x + 1
the other side. 2
1
Step 3. Now simplify both the side again. Þ 10x - 3x =
2
Step 4. Use the four rules to find the value
(Transfer 3x from right hand side to the left
of the variable.
hand side, then positive 5x changes to
Note: When we change the sides of numeral and negative 3x).
variable terms, the following rules are followed: 1
Þ 7x =
4
+ changes to -, 2x + 4 = 8 Þ 2x = 8 - [See, +4 2
changes to -4 ]
7x 1
- changes to +, 2x - 4 = 8 Þ 2x = 8 + [See, -4 Þ = ÷ 7 (Divide both
4
changes to +4 ] 7 2
12 sides by 7)
´ changes to ¸, 2x = 12 Þ x = [See, 2 ´ x changes
2 1 1
12 Þ x = ´
to ] 2 7
2
1
x x Þ x =
¸ changes to ´, = 12 Þ 12 ´ [See, = changes to
2
2 2 4
12 ´ ] 1
2
Therefore, x = is the solution of the given
14
Example 1: Solve the equation 4x - 1 = 24 - x.
equation.
Solution:
Example 3: Solve the equation 5(x - 2) + (x -3 )
4x - 1 = 24 - x
= 2(2x + 1) - 9 and verify your answer
Þ 4x + x = 24 + 1
Solution:
[ Transfer -x from right hand side to the left
5(x - 2) + (x - 3) = 2(2x + 1) - 9
hand side, then negative x changes to positive
Þ 5x - 10 + x - 3 = 4x + 2 - 9
x. Similarly again transfer -1 from left hand
Þ 6x - 13 = 4x - 7
side to the right hand side, then negative 1
change to positive 1.Therefore, we arranged Þ 6x - 4x = -7 + 13
the variables on one side and the numbers on Þ 2x = 6
the other side.] 6
Þ x =
Þ 5x = 25 2
5x 25 Þ x = 3
Þ = (Divide both
5 5 Therefore, x = 3 is the solution of the given
sides by 5) equation.
Þ x = 5 Now we will verify both the sides of the
equation,
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Mathematics In Focus - 8