Give first the step you will use to separate the
variable and then solve the equation.
Answers
Required Answer
How to separate the variable and solve the equation?
Answer: Let us take a simple example [ 5x - 2 = 3x ]
1. When we transpose the equations, the sign changes to the opposite. The transposing equations can be made as:
- + ➪ -
- - ➪ +
- ÷ ➪ ×
- × ➪ ÷
2. After this we apply the integer rule here.
- - - = +
- + + = +
- + - = -
- - + = -
3. Keep this in mind that if we ae adding/subtracting 2 numbers such as:
- [-2 + 1] , we will write the sign of the greater number here, i.e. [-1]
- [-2 - 1] , we will write the sign of the greater number here again, i.e. [-3]
- [-2 + (-1)] , we will write the sign of the greater number here, i.e. [-3]
- [+2 + 1] , we will write the sign of the same sign here because both are same, i.e. [+3]
4. Now let us solve the given example equation by transposing.
- [ 5x - 2 = 3x ]
5. Here let us first transpose the variable numeral. First transpose 5x to the right side. As the sign will change to minus here. (Here we can also cancel minus because same sum in the opposite places can be cancelled i.e. 2 = 2× x)
- -2 = 3x - 5x
- -2 = -2x
- -2 = -2 × x or
- 2 = 2 × x
6. Now we will transpose -2 from right to left and will leave variable at right only. As we know that -2 will come to left in division because it multiplied with x on the right. We can cancel the minus signs here.
- -2/-2 = x or
- 2/2 = x
- 1 = x
So, here we got the value of x as 1.
This was a simple and basic example taken for understanding. There can be more complex examples too . For extra information see these questions:
- https://brainly.in/question/34996698
- https://brainly.in/question/34981808
The number 1 will be moved to RHS of equation with suitable change in sign.
So,
x
–
1
=
0
Or,
x
=
0
+
1
=
1
x
+
1
=
0