Everything under the sun focuses on a particular type of balance. Even when the balance shifts to one side while you are cycling, you are likely to fall. It is mainly because the overall balance changes and causes collapse.
However, it is the same some mathematical equations as well. By now, you must have come across the ‘equal to’ sign (=) more than you can count. Like everything else, an equation has to be balanced as well. So, where can you put simple equations in this context? This article will help you to do just that.
In the simplest of terms, a variable and an ‘equal to’ sign make up a simple equation. Therefore, a simple equation is a mathematical representation of two expressions on either side of an ‘equal to’ sign.
It mostly consists of a variable, frequently accompanied by a numerical constant. To understand this concept easily, consider the following example.
3x – 4 = 5. It is a class 7 simple equation. In this representation, the x refers to a variable. Every equation of this category aims to find the value of x. However, you can also use other letters from the English alphabet to write a variable.
Moreover, the value of 3x – 4 has to be equal to 5. Therefore, a simple equation of class 7 maintains the same value on either side of the ‘=’ sign.
In this case, you can shift any number or variable from one side of the equation to the other. However, you have to keep in mind that the sign preceding the number changes as well. For example, a number with a negative integer transforms into a positive integer when it shifts to the other side.
Coming back to this equation, you can take -4 to the other side in the following way –
3x = 5+4 = 9.
Therefore, x = 9/3 = 3. Thus, the value of the variable x is 3.
Solve the Sum
In the simple equation 5x – 4 = 16, find the value of x.
An equation stands as 10y + 25 = 125. Find the value of the variable y.
Now you know what a simple equation means. However, before solving simple equations, you will have to understand what transposition stands for.
What is Transposition in a Simple Equation?
In its most primary sense, transposition implies when you shift a variable or a number to the other side of ‘=’. It is one of the most vital functions of simple equation sums.
To be able to understand this further, you will have to keep in mind the signs preceding a variable or a number. As you shift a number to the other section; its sign changes. For instance, ‘+’ becomes ‘-‘ and ‘-‘ turns into ‘+’ when it changes sides.
Consider the following example –
50x – 20 = 980.
Therefore, 50x = 980+20
50x = 1000
x = 1000/50
Or, x = 20.
As you can see in this particular simple equation in mathematics, -20 becomes +20 on the other side. It refers to an easy example of transposition.
In the next section, you will learn about the real-life applications of simple equations.
Suppose you have Rs.1000, out of which you can spend Rs.300 on video games. With the remaining money, you will have to purchase some books from a particular series. After reaching the market, you see that each book costs Rs.70.
So, how many books should you buy so that you still have Rs.300 left for video games? It is where simple equations class 7 standard will come to your rescue.
Assume that x stands for the number of books you can buy at Rs.70 per book. Therefore, the equation becomes –
70x + 300 = 1000
70x = 1000-300
70x = 700
x = 700/70
Therefore, x = 10. Thus, you can buy 10 books @Rs.70 and still be able to keep Rs.300 for your video games. However, you should also know about solving simple equations with fractions.
Take into account the following example of a simple equation with fractions –
½ x + ⅘ = 1 ⅙
So, how will you find the value of x in this equation? Transpose ⅘ to the other side and convert the mixed fraction into an improper fraction.
Therefore, 1/2 x = 7/6 - 4/5
½ x = ((7x5) - (4x6))/30 , since the LCM of 5 and 6 is 30.
½ x = (35-24)/30
½ x = 9/30 = 3/30
x = 3/10 X 2
Therefore, the value of x is 3/5.
Now that you know about this concept, it is time to take a look at simple equation exercises.
Solve the following NCERT maths class 7 simple equations to improve and sharpen your understanding –
Write the following statements in the form of simple equations:
The sum of five times y and 15 is 32.
One-third of a number plus 5 is 8.
Consider the following equation:
Shyam’s father’s age is 5 years more than three times Shyam’s age. Shyam’s father is 44 years old. Set up an equation for this situation and find Shyam’s age.
This article, therefore, sheds light on the definition, example, and nature of simple equations. However, you can look out for other similar interesting topics on the website of Vedantu. You can also download our Vedantu app for enhanced access.
1. What Is A Simple Equation?
A simple equation refers to a mathematical equation that expresses the relationship between two expressions on both sides of the ‘equal to’ sign. This category of an equation consists of a variable, usually in the form of x or y.
Solving simple equations often require rearranging it. In such cases, you need to introduce the terms other than X on one side and all the numbers on the other side. This method is known as the process of isolating X.
Any mathematical operation performed on one side of the equation requires exact mirroring of it on the other side. It is essential to preserve the relationship between both sides of the equation.
2. What Is A Variable?
Variable means an unknown factor in an equation that a simple equation aims to find out. An equation can also have multiple variables, in which case it will be known as a quadratic equation.
Variables play different roles in different mathematical formulas. It can be identified via various specific names, such as an indeterminate variable, which appears in a formal power series. It is a constant with a ring of polynomial, and is considered as a special kind of variable.
Parameters are also a type of variable which remains constant regardless of any mathematical operation. It carries different meaning for mathematics and computer science.
3. What Is The Example Of A Simple Equation?
The example of a simple equation is 4x - 15 = 25.
Letters that are used to substitute for numbers in algebra is known as variables. However, there are certain letters and symbols that substitute for a fixed value in a simple equation (such as pi, which is always 3.142). these are known as constants. Usually, in simple algebraic equations, numbers and letters stay constant throughout the mathematical operation.
4. What Kinds Of Fraction Can Be Present In A Simple Equation?
Proper, improper and mixed fractions can be present in a simple equation.
Proper fractions carry numerators that are smaller than their denominators. Improper fractions carry numerators and denominators that are either equal to or greater than each other (numerator > denominator).
Mixed fractions are a combination of proper fraction and whole number. You will have to solve a number of problems involving proper, improper, and mixed fraction in this chapter.