Linear Equation in One Variable: An equation is called linear equation if it has only one degree i.e., the highest power of the variable appearing in equation is 1, and the form of linear equation is
P(x) = ax + b = 0 , e.g.
x + 5 = 0
A number which satisfies an equation is called the solution of the equation.
A term may be transposed from one side of the equation to the other side, but its sign will be changed.
Stepwise procedure to solve a word problem.
- Read the given word problem carefully and identify what is given and what is required.
- Use letters x, y, z, etc. to represent the unknown quantity.
- Transform the statements of the problem into mathematical statements.
- Form the linear equation according to the given condition (s) of the problem.
- Solve the equation by the usual method.
- Check the solution for its validity.
- Reject if the solution is invalid.
Solving Equations having the Variable on Both Sides
We transpose the terms in such a manner that the terms containing the variables are on the LHS and constant numbers on RHS.
Then, simplifying both sides and dividing by a suitable number (if required), we can solve the equation.
Finally, check the validity of the solution obtained. Reject if the solution is invalid.
Reducing Equations to Simpler Form
We multiply both sides of the equation by the LCM of the denominators of the terms in the expressions occurring in the given equation.
We transpose properly so that all the variable terms come on LHS and constant terms on RHS.
Then, combining like terms on both sides of the equation and dividing both sides by a suitable number (if required), we can find out the required solution.
Finally, we check this solution for its validity. Reject if the solution is invalid.
Equations Reducible to Linear Form
Sometimes the given equation is not linear in form. By cross-multiplication and further simplification, it can be transformed into a linear equation in one variable. Then, it can be solved by the usual method.