Simple Equations -Grade-07



Equations

Equation is a mathematical expressions connected with equal operator.

Normally an equation always have a variable. Variable is a letter in an equation and it can vary its value n different time. So now we can says that an equation is the condition on variable.

for example 4x +5=17, Here x is the variable.

An equation always have a equal operator and  one LHS and one RHS. The equation will only satisfied (true) when LHS =RHS.

In order to satisfy an equation, the variable in the equation should have a particular value.

The value of the variable in which the equation will satisfy is called solution of the equation.

The process to finding out the solution of the equation is called solving the equation.

Now we can practice to convert some conditional statement to equation

The sum of three times x and 11 is 32

3x+11=32

If you subtract 5 from 6 times a number., you get 7

6x-5=7

One fourth of m is 3 more than 7

m/4=3+7 or m/4-7=3

One third of a number plus 5 is 8

n/3+5=8

Now we can practice to make conditional statement from an equation 

x-5=9,  5p=20, 3n+7=1, (m/5)-2=6

First one is, subtracting 5 from a number is 9. Other equation you can practice.

Raju’s father’s age is 5 more than 3 times raju’s age. If raju’s father have 44 year old . Set Up an equation and find raju’s age.

We can also practice same type of other questions.

Solving an equation

The following points we can keep it in our mind to solve an equation.

  1. All ways the LHS and RHS will be same in value.
  2. Equations will still valid if we add same number to RHS and LHS.
  3. Equations will still valid if we subtract same number from LHS and RHS
  4. Equations will still valid if we multiply or divide same number in LHS and RHS

If we  move any value fRom LHS to RHS or RHS to LHS we have to follow the below mentioned



Transposition rules
  1. The adding value will subtract in opposite side.
  2. The subtracting value will add in the opposite side.
  3. The multiplication value will divide in the opposite side.
  4. The dividing value will multiplied in the opposite side.

First we have to practice solving the equation by separate the variable and  solve the equation. For this method we are not using the transposition method, but we will add, subtract, multiply or divide both side in such a way that  the variable will be separated by cancel the other terms with the variable.

for example x-1=0, here we can add 1 to both side, so that the -1 will be cancelled in the LHS and we will get the value of the x. we can practice such a exercise from test book.

We can also solve the equation by transposition method. For solving by this method please follow the transposition rules mentioned above. We can also practice the exercises for this method.

From solution to equation

Finding a solution from the equation is called normal path. So we move on reverse path, that means from the solution steps back to equation.

If we have a solution like x=5 or y=9, from this we can obtain their equations. To find the equation from solution we can add, subtract, multiply or divide equal numbers on the both side of the solution.

for example x=5,      x+2=5+2 ,   which can write as x+2=7 (is an equation).

We can also see that a single solution can have any number of equations. Now please practice the exercises.

application  of simple equation in practical situation

As we already seen we can convert the actual  situation to an equation. And hence we can solve the equations as we studied. Now we can do the exercise for dealing with more practical situations and learn how to solve them.




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