Slide 1 : What is an Equation? A statement which shows that two quantities are EQUAL, is called an EQUATION. For Example:
2x = 10
2x2 + 3y = 16
7a - 2b + 5 = 2ab + 23
Slide 2 : What is Simple Linear Equation? An Equation which contains only one variable with one degree is called a SIMPLE LINEAR EQUATION in One Variable. For Example:
2x - 4 = 10 Following are not Simple Linear Equation in One Variable :
2x - 4 = 10y 5x - 2 = 16 7 - 2b + 5 = 2b 5x3 - 2 = 16 7a - 2b + 5 = 2b
Slide 3 : How to solve a Simple Linear Equation? The method of finding the value of the variable which makes the equation true, when substituted in it, is called Solving The Equation. This value of the variable is called the root of the equation. There will be only one root for a simple linear equation in one variable. Equation is similar to a weighing balance in which the weights on left hand side and right hand side of the pivot are equal in balancing condition. If we add some extra weight at any one side of the weighing balance, then the balance will disturb. We have to add the same weight to the another side to maintain the balance. Similarly, if we remove some weight from any one side of the weighing balance, then also the balance will disturb and we have to remove the same weight from the another side to maintain the balance.
…contd.
Slide 4 : How to solve a Simple Linear Equation? An equation is solved by using the properties of weighing balance, according to which:
When equal quantities are added to both sides of an equation, the statement remains unchanged. If 2x + 7 = 5x – 1
then, 2x + 7 + 3 = 5x – 1 + 3 is also same. If 2x + 7 = 5x – 1
then, 2x + 7 + 9x = 5x – 1 + 9x is also same.
Slide 5 : How to solve a Simple Linear Equation? An equation is solved by using the properties of weighing balance, according to which:
2. When equal quantities are subtracted from both sides of an equation, the statement remains unchanged. If 2x + 7 = 5x – 1
then, 2x + 7 - 3 = 5x – 1 - 3 is also same. If 2x + 7 = 5x – 1
then, 2x + 7 - 9x = 5x – 1 - 9x is also same.
Slide 6 : How to solve a Simple Linear Equation? An equation is solved by using the properties of weighing balance, according to which:
3. When both sides of an equation are multiplied by equal quantities, the statement remains unchanged. If 2x + 7 = 5x – 1
then, 3(2x + 7) = 3(5x – 1) is also same.
Slide 7 : How to solve a Simple Linear Equation? An equation is solved by using the properties of weighing balance, according to which:
4. When both sides of an equation are divided by equal quantities, the statement remains unchanged. If 2x + 7 = 5x – 1 Then , is also same.
Slide 8 : Exercise 1: Solve: 4x + 10 = 2x + 16 Subtract 2x from both the sides:- 4x + 10 – 2x = 2x + 16 -2x Or, 2x + 10 = 16 Now, subtract 10 from both the sides:- 2x + 10 -10 = 16-10 Or, 2x = 6 Now, divide both the sides by 2:- Or, x = 3 is the answer.
Slide 9 : Exercise 2: First of all, multiply both the sides of equation by 6:- Or, 2(2x) = x+9
Or, 4x = x+9 Now, subtract x from both the sides:- 4x -x = x+9 -x Or, 3x = 9 Now, divide both the sides by 3:- Or, x = 3 is the answer.
Slide 10 : Exercise 3: First of all, cross multiply both the sides of equation :- Or, 8x + 16 = 24x -48 Now, subtract 24x from both the sides:- 8x + 16 -24x = 24x-48 -24x Or, 16 - 16x = -48 Now, Subtract 16 from both the sides:- Or, x = 4 is the answer. Or, 16 - 16x - 16 = -48 - 16 Or, - 16x = -64 Now, Divide both the sides by -16:-