If a, b, c are real numbers and x is variable, equation 

ax + b = c, a\ne 0

is called a linear equation. Each equation has a left hand side and a right hand side. Both sides contain either numerical or algebraic expression. In case of linear equation, power/index of the variable is never more than one. If the variable is replaced by a number, that number is called the value of that variable. After substituting the value of the variable, if both sides of the equation are equal then the equation is said to be satisfied (true) for the variable.

The number which satisfies the given equation is called the solution of the equation. Solve the equation means the find the value of the variable in that equation.

We use 4 operations to solve the equation

  1. By adding the same number/term on both sides
  2. By Subtracting the same number/term from both sides
  3. By multiplying both sides the same non-zero number
  4. By dividing both sides by the same non-zero number
  1. Solve the equation
7\left(x+5\right)+6\left(2x+1\right)=9\left(x+3\right)+4\left(x+5\right)
             7x + 35 + 12x + 6=9x + 27 + 4x + 20
                     19x + 41 = 13x + 47
                      6x + 41 = 47  ---subtract 13x both sides)   
                           6x = 6  --- subtract 41 both sides
                            x = 1     

  2. Solve for p     
\frac{4p+1}{6\:}-\frac{2p-4}{3}\:=\:-\frac{3p}{4}
                          What is LCM of 6, 3 and 4? 
LCM is 12
Multiply all the terms by 12
12\left(\frac{4p+1}{6\:}\right)-12\left(\frac{2p-4}{3}\right)\:=\:12\left(-\frac{3p}{4}\right)
 simplify to remove fractional form we get
         2(4p+1)-4(2p-4) = 3(-3p)
               8p+2-8p+16= -9p 
                       18= -9p
                       -2= p
                        p= -2

3. Solve for x

3x-12=\frac{2x}{3}+16
             Multiply all the terms by 3
                  9x-36 = 2x + 48
                  7x -36= 48 subtracted 2x both sides
                   7x   = 84  added 36 both sides
                    x = 12  Answer!

4. If 0.6x+0.8 = 0.28x + 1.16, what is the value of x?

         0.32x + 0.8 = 1.16
             0.32x   = 0.36
                    x= 1.125
5. Solve for z

\frac{2-3z}{15-4z}=\frac{2}{3}

Cross multiply

                             3(2-3z) = 2(15-4z)
                              6-9z =30-8z  distributive property
                               6-z = 30  added 8z both sides
                               -z = 24   subtracted 6 both sides
                                z= -24   Answer!

Practice Worksheet