Hello friends as you all know grade V algebra is part of algebra 1, which is the very first step towards the learning of algebra (take help of algebra calculator also). In the previous articles we have learnt several different topics of algebra that you study in grade v. Grade v is generally the last class of primary group. In this article we will discuss the last topic of grade V algebra. Today I will make you familiar with the interesting algebra topics one is equations and other is inequalities. Equation and inequalities are the basic of algebra and whole algebra moves around both the topics. Not only in grade V but also in higher grades you will learn both the topics.
Equations are defined as the two mathematical statements that are joined together with an equal to symbol. Equal symbol is the main sign by which you can easily identify the equation. In equation we deal with numbers, variables, constant and mathematical operators along with equal to symbol (=). There are several different types of equations which you learn when you move to different grades. Whenever we have to solve any equation, first of all we always try to isolate the variables, so that we can easily and simply get the solution of the problem. Equations are even used when we solve complex words problems also, as it is hard to understand the word problem and solve them. So first we try to take the word problem in form of equations and then put the valid method on the given equation and find the answer or solution of the problem.
Now move towards the principle that we use while solving equations,
1. The addition principle: according to this principle you can say that when a = b,
a + c = b + c for any number c.
Here is an example so that my students can easily understand this concept,
Solve: a + 6 = - 15
Using the above mentioned principle add – 6 to both the sides and try to find the value of the variable.
a + 6 – 6 = - 15 – 6,
The variable is now isolated,
Thus, a = - 21.
This is all about the addition principle.
2. The next principle is called as multiplication principle. In this principle is if a = b. and c is any number,
a * c = b * c. this principle is also used to help to isolate the variable that you are asked to solve or whose value you have to calculate.
Example: solve 4p = 9,
Using the multiplication principle we can easily the problem as:
Multiply both the sides of the equation by (1/4)
So doing this we get,
(1/4). 4x = ( ¼) . 9
By doing this we have isolated the
x = (9/4)
Also, be aware of problems where you might need to use both of these principles together.
Now have an example showing both the above described properties i.e. addition principle and the multiplication principle.
Example: solve the given equation and find the value of x?
3x - 4 = 13
Solution: first Use the Addition Principle to simplify the equation,
add 4 to each side.
3x - 4 + 4 = 13 + 4
After simplifying, 3x = 17.
Now, use the multiplication principle and get the final answer or value of the variable,
Using the multiplication principle we get,
multiply each side by (1/3).
(1/3)3x = (1/3)17
After simplification, the variable is isolated
x = (17/3).
Here are few more examples of equations so that you can easily grasp the concept of how to solve equations.
example: x + 2 = 4,
solution, apply addition principle, on doing so we get,
x+2 -2 = 4 - 2,
x = 2, thus variable x = 2.
example: 2x + 4 = 8,
solution: 2x + 4 -4 = 8 -4,
2x = 4,
multiply by 1/2,
1/2 * 2x = 1/2 * 4,
x = 2,
thus we use both addition and multiplication principle and get the naswer of the variable as 2.
Example
Solve the equation for the variable x: x- 20 = 30
Solution:
x - 20 = 30
Add 20 on both sides of the equation
x – 20 + 20 = 30 + 20
x = 50
So, the answer is y = 50.
example:
Solve the equation for the variable x: (q/3) + 40 = 30
Solution:
(q / 3) + 40 = 30
Subtract 40 on both sides of the equation
(q / 3) + 40 - 40 = 30 - 40
(q / 3) = -10
Multiply 3 on both sides of the equation
(q / 3) * 3 = -10 * 3
q=-30
So, the answer is 30.
Now, move to the next important topic that we will learn today i.e. inequalities. The term inequality means the mathematical phrases are not joined with help of equal to symbol. To describe any inequality we always take the inequalities symbol. Generally we have four types of inequality symbol,
> : greater than,
<Less than,
<= less than equal to and the last is,
>= greater than equal to,
Whenever you get these types of symbols understand that the given expression shows the inequality and whenever you get the equal to symbol then understand that it is an equation.
Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign. Let’s have few example of inequalities to get the concept of how to solve the inequalities problem.
Example:
Solve the inequality: 8y + 5 < 6y +7.
Solution:
We have, 8y + 5 < 6y +7
Subtract 6y on both sides of the equation
8y – 6y + 5 < 6y + 7 – 6y
2y + 5 < 7
Subtract 5 on both sides of the equation
2y+ 5 – 5 < 7 – 5
2y < 2
Divide by 2 on both sides of the equation
y< 1
So, all the numbers are lesser than 1.
Hence, the solution set is (-infinity, 1).
Example:
Solve the inequality: -2p – 8 < 6
Solution:
-2p-8<6
Add 8 on both sides of the equation
-2p - 8 + 8 <6 + 8
-2p < 14
Divide by-2 on both sides of the equation and the inequality sign is to be reversed.
p > -7
So, all the real numbers which are greater than -7. Hence, the solution set is (-7, infinity).
Solving linear inequalities is almost exactly like solving linear equations
Solve x + 3 < 0.
If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:
X<-3
Then the solution is:
x < –3.
Inequalities problem may have infinite number of solutions. we get the solution of inequalities only when we have true statement. Solving an inequality is simple due to the movement of number and variable from one side to other. Whenever you solve linear inequalities we flip the the inequality sign and simply solve the problem and get all possible solution of the problem.
This is all about the equations and inequalities. Friends! today we have finished all the algebra topics of grade V Tamilnadu education board that you study in this grade. In the next coming article we will focus on the remaining branches of Grade V mathematics that includes, geometry, number system, and many other branches. Students if you still have any problem In any of the topic that I taught then you can ask your problems and queries to me. Mathematics is that subject which needs lots of practice and if you do practice on daily basis then you can solve all the different types of math problems and become master of the subject. Try to solve all the problems of mathematics daily and clear all your doubts with my help, or your teachers. To become master of subject you need to practice different topics daily. If you do so then no one can beat you in such a wonderful subject and you will get good grades.
In upcoming posts we will discuss about Math Blog on Grade V. Visit our website for information on integral calculator
Equations are defined as the two mathematical statements that are joined together with an equal to symbol. Equal symbol is the main sign by which you can easily identify the equation. In equation we deal with numbers, variables, constant and mathematical operators along with equal to symbol (=). There are several different types of equations which you learn when you move to different grades. Whenever we have to solve any equation, first of all we always try to isolate the variables, so that we can easily and simply get the solution of the problem. Equations are even used when we solve complex words problems also, as it is hard to understand the word problem and solve them. So first we try to take the word problem in form of equations and then put the valid method on the given equation and find the answer or solution of the problem.
Now move towards the principle that we use while solving equations,
1. The addition principle: according to this principle you can say that when a = b,
a + c = b + c for any number c.
Here is an example so that my students can easily understand this concept,
Solve: a + 6 = - 15
Using the above mentioned principle add – 6 to both the sides and try to find the value of the variable.
a + 6 – 6 = - 15 – 6,
The variable is now isolated,
Thus, a = - 21.
This is all about the addition principle.
2. The next principle is called as multiplication principle. In this principle is if a = b. and c is any number,
a * c = b * c. this principle is also used to help to isolate the variable that you are asked to solve or whose value you have to calculate.
Example: solve 4p = 9,
Using the multiplication principle we can easily the problem as:
Multiply both the sides of the equation by (1/4)
So doing this we get,
(1/4). 4x = ( ¼) . 9
By doing this we have isolated the
x = (9/4)
Also, be aware of problems where you might need to use both of these principles together.
Now have an example showing both the above described properties i.e. addition principle and the multiplication principle.
Example: solve the given equation and find the value of x?
3x - 4 = 13
Solution: first Use the Addition Principle to simplify the equation,
add 4 to each side.
3x - 4 + 4 = 13 + 4
After simplifying, 3x = 17.
Now, use the multiplication principle and get the final answer or value of the variable,
Using the multiplication principle we get,
multiply each side by (1/3).
(1/3)3x = (1/3)17
After simplification, the variable is isolated
x = (17/3).
Here are few more examples of equations so that you can easily grasp the concept of how to solve equations.
example: x + 2 = 4,
solution, apply addition principle, on doing so we get,
x+2 -2 = 4 - 2,
x = 2, thus variable x = 2.
example: 2x + 4 = 8,
solution: 2x + 4 -4 = 8 -4,
2x = 4,
multiply by 1/2,
1/2 * 2x = 1/2 * 4,
x = 2,
thus we use both addition and multiplication principle and get the naswer of the variable as 2.
Example
Solve the equation for the variable x: x- 20 = 30
Solution:
x - 20 = 30
Add 20 on both sides of the equation
x – 20 + 20 = 30 + 20
x = 50
So, the answer is y = 50.
example:
Solve the equation for the variable x: (q/3) + 40 = 30
Solution:
(q / 3) + 40 = 30
Subtract 40 on both sides of the equation
(q / 3) + 40 - 40 = 30 - 40
(q / 3) = -10
Multiply 3 on both sides of the equation
(q / 3) * 3 = -10 * 3
q=-30
So, the answer is 30.
Now, move to the next important topic that we will learn today i.e. inequalities. The term inequality means the mathematical phrases are not joined with help of equal to symbol. To describe any inequality we always take the inequalities symbol. Generally we have four types of inequality symbol,
> : greater than,
<Less than,
<= less than equal to and the last is,
>= greater than equal to,
Whenever you get these types of symbols understand that the given expression shows the inequality and whenever you get the equal to symbol then understand that it is an equation.
Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign. Let’s have few example of inequalities to get the concept of how to solve the inequalities problem.
Example:
Solve the inequality: 8y + 5 < 6y +7.
Solution:
We have, 8y + 5 < 6y +7
Subtract 6y on both sides of the equation
8y – 6y + 5 < 6y + 7 – 6y
2y + 5 < 7
Subtract 5 on both sides of the equation
2y+ 5 – 5 < 7 – 5
2y < 2
Divide by 2 on both sides of the equation
y< 1
So, all the numbers are lesser than 1.
Hence, the solution set is (-infinity, 1).
Example:
Solve the inequality: -2p – 8 < 6
Solution:
-2p-8<6
Add 8 on both sides of the equation
-2p - 8 + 8 <6 + 8
-2p < 14
Divide by-2 on both sides of the equation and the inequality sign is to be reversed.
p > -7
So, all the real numbers which are greater than -7. Hence, the solution set is (-7, infinity).
Solving linear inequalities is almost exactly like solving linear equations
Solve x + 3 < 0.
If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:
X<-3
Then the solution is:
x < –3.
Inequalities problem may have infinite number of solutions. we get the solution of inequalities only when we have true statement. Solving an inequality is simple due to the movement of number and variable from one side to other. Whenever you solve linear inequalities we flip the the inequality sign and simply solve the problem and get all possible solution of the problem.
This is all about the equations and inequalities. Friends! today we have finished all the algebra topics of grade V Tamilnadu education board that you study in this grade. In the next coming article we will focus on the remaining branches of Grade V mathematics that includes, geometry, number system, and many other branches. Students if you still have any problem In any of the topic that I taught then you can ask your problems and queries to me. Mathematics is that subject which needs lots of practice and if you do practice on daily basis then you can solve all the different types of math problems and become master of the subject. Try to solve all the problems of mathematics daily and clear all your doubts with my help, or your teachers. To become master of subject you need to practice different topics daily. If you do so then no one can beat you in such a wonderful subject and you will get good grades.
In upcoming posts we will discuss about Math Blog on Grade V. Visit our website for information on integral calculator
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