Notes - Linear Equation in one variable
Category : 7th Class
LINEAR EQUATION IN ONE VARIABLE
FUNDAMENTALS
Symbols used to denote a constant are generally, 'c', 'k' etc...
e.g., 2x - 6; here, 2 is the coefficient of \['x';\,\,'x'\] is the variable and \[-6\]is the constant. Similarly in \[ay+b;\,\,a\] is the coefficient of \[y;\,\,'y'\] is the variable and \[(+b)\] is the constant.
e.g., (i) \[5x-1=6x+m\] (ii) \[3\left( x-4 \right)=5\]
(iii)\[2y+5=\frac{y}{6}-2\] (iv) \[\frac{t-1}{6}+\frac{2t}{7}=a\]
e.g., \[2x+6=3x-10\Rightarrow 6+10=3x-2x\Rightarrow 16=x\]
Verification
Substituting \[x=16\] we have LHS \[=2\times 16+6=38\] & RHS \[=\text{ }3\times 16-10=38\]
\[\therefore \]\[x=16\]is a solution of the above equation.
(a) Same number can be added to both sides of an equation.
(b) Same number can be subtracted from both sides of an equal.
(c) Both sides of an equation can be multiplied by the same non - zero number
(d) Both sides of an equation can be divided by the same non - zero number
(e) Cross multiplication: If\[\frac{ax+b}{cx+d}=\frac{p}{q}\], then \[q\left( ax+b \right)=p\left( cx+d \right).\]
This process is called cross multiplication.
You need to login to perform this action.
You will be redirected in
3 sec