Category : 8th Class
Linear Equations in One Variable
The general form of a linear equation in variable x is
a\[x\]+ b = 0, a\[\ne \]0 or px = q, p \[\ne \]0
(i) The same quantity may be added to or subtracted from both sides of an equation without changing the equality.
Thus, if a = b,
a +c= b +c
a - c= b – c
(ii) If a = b then a - b = 0 (or b - a = 0).
That is, given an equality any term from one side may be transfered to the other side by changing its sign. (Law of transposition)
(iii) lf a= b then ac = be \[\frac{a}{c}=\frac{b}{c}\],(c\[\ne \]0).
That is, given an equality, both the sides can be multiplied by the same number or divided by the same nonzero number.
If \[\frac{a}{c}=\frac{b}{c}\]then multiplying both sides by bd we have ad = bc. (rule of crosswise multiplication)
(iv) If ac = be a = b provided c\[\ne \] 0. (Law of cancellation)
That is, both sides of an equality can be divided by the same nonzero number.
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