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Math Equations are equations that connect two algebraic expressions by an equal sign (=). Math Equation is a term or statement which is used to identify the unknown value of the variable. A math equation is made from variables, constants, coefficients, operators, and expressions. For example, 5x + 5 = 10 is a math equation. Math equations are used to find out the value of an unknown variable in a particular expression. Math Equations may contain a single or more than one algebraic expression. Based on the expression, math equations are categorized into Linear Equations, Quadratic Equations, Radical Equations, Exponential Equations, and Rational Equations.
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Key Terms: Math Equations, Algebraic Expressions, Equations, Linear Equations, Quadratic Equations, Exponential Equations, Variable
What is Math Equation?
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Math equation is defined as a mathematical statement having an equal symbol in the middle of the algebraic equation. It is also known as an algebraic expression. They are statements that hold the equality of two algebraic expressions. The expressions on both sides are considered the left-hand side and right-hand side of the equation. Math equations play an integral part in Mathematics.
Example of Math Equation: 3x - 6 =15 is a math equation.
3x - 6 is the expression on the left-hand side, which is equal to the expression 15 on the right-hand side.
Here,
- 3 is the Coefficient.
- x is the Variable.
- - is the Operator.
- 6,15 are Constants.
Math Equation
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Different Types of Equations
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Math equations can be categorized into the following types:
- Quadratic Equation
- Linear Equation
- Radical Equation
- Exponential Equation
- Rational Equation
Linear Equation
In linear equations, each term is either a constant or single variable or a product of a constant. The general form of linear equations with two variables is as follows:
Y = mx + c, m ≠ 0
Here, m is the slope while C is the point on which it cut the y-axis.
Examples of Linear Equation
- 2x + 4 = 0 (linear equation in one variable)
- 3a + 5b + 8 = 15 (linear equation in two variables)
Quadratic Equation
It is a type of equation in which one of the variables holds an exponent of 2. Quadratic equations can be represented in the general form as
ax2 + bx + c = 0, a ≠ 0
Example of Quadratic Equation: 5x2 – 5y - 35=0
Here
- a = 5
- b =-5
- c =-35
Read More: Quadratic Equations MCQs
Radical Equation
The equation in which the variable is lying inside a square root symbol or you can say that the maximum exponent on a variable is ½ is known as a radical equation.
Example of Radical Equation: √a + 16 = 26
Read More: Radicals
Exponential Equation
This is a type of equation that holds the variables instead of any numerical exponents. We need to use various properties to solve exponential equations:
Rational Equation
It is a type of equation that contains rational expressions. It is represented as
a/2 = a+2/ 4
It simply has a numerator and denominator.
Example of Math Equations
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Here is a math equation that can be solved step-by-step:
Example: What will be the solution of the given math equation and verify the answer?
4x – 7 (2-x) = 3x + 2
Solution: 4x – 7 (2-x) = 3x + 2
Simplify the left side of equation,
4x – 14 + 7x = 3x + 2
11x – 14 = 3x + 2
Transporting all the ‘x’ terms on one side and constant term on other side
11x-3x = 14 + 2
8x = 16
X = 16/8
X = 2
Thus, the solution for the given equation 4x – 7 (2-x) = 3x + 2 is 2
Verification
We will substitute x = 2 in the equation.
4x – 7 (2-x) = 3x + 2
4(2) – 7 (2-2) = 3(2) + 2
8 – 7(0) = 6 + 2
8 = 8
L.H.S = R.H.S
Hence verified.
Read More:
| Related Topics | ||
|---|---|---|
| Radical Formula | Exponential Formula | Difference Between Power And Exponent |
| Square Root Formula | Integers as Exponents | Discriminant |
Things to Remember
- Math Equation is defined as a mathematical statement that consists of two algebraic expressions.
- Math equations are made up of variables, coefficients, operators, constants, terms, expressions, and an equal sign.
- There are different types of math equations that contain more than one/two expressions.
- Math equations included in algebra are quadratic equations, linear, radical, exponential, and rational equations.
- Math Equations should contain an "=" equal sign and terms on both sides.
Sample Questions
Ques. Solve the given equation and verify the answer. (3 Marks)
2x – 6(2 - x) = 3x + 2
Ans. First, we will simplify the given equation:
2x – 6(2 - x) = 3x + 2
2x – 12 + 6x = 3x + 2
8x = 3x + 14
8x - 3x = 14 = 5x = 14
x = 14 / 5
Thus, the solution for the given equation 2x – 6(2 - x) = 3x + 2 is 14/5.
Verification
Substitute the value of x = 14/5 in the given equation 2x – 6(2 - x) = 3x + 2;
2(14/5) – 6(2 - 14/5) = 3(14/5) + 2
28 / 5 + 24 / 5 = 52/5
28 + 24 = 52
52 = 52
L.H.S = R.H.S
Hence verified.
Ques. Solve the given math equation 3x – 5 = 16. Verify the same. (3 Marks)
Ans. Given equation is 3x – 5 = 16
Transporting constants on one side;
3x = 16 + 5
3x = 21
Shifting 3 on RHS
x = 21/3
x = 7
Verification:
Substituting x = 7 in 3x – 5 = 16,
LHS = 3x – 5
= 3 x 7 - 5
= 21 - 5
= 16
RHS = 16
LHS = RHS
Hence Verified.
Ques. What is a linear equation? (3 Marks)
Ans. Each term involved in the linear equation is either a constant or single
variable or a product of a constant. The general form of linear equations
with two variables is given by
Y = mx + c , m ≠ 0
Where
- m is the slope
- C is the point on which it cuts the y-axis.
Example of Linear equation with one variable : 30x– 60 = 0
Linear equations with two variables : 3y - 5x + 2=0
Ques. How many types of equations are there? (3 Marks)
Ans. Some of the lists of math equations involved in algebra are as follows
given below.
- Quadratic Equation
- Linear Equation
- Radical Equation
- Exponential Equation
- Rational Equation
- Linear Equations
Ques. What are Quadratic Equations? (2 Marks)
Ans. The quadratic equation is a second-order equation in which any one of
the variables contains an exponent of 2.
Example: 5x2 + 7 = 54, here the variable has a power of 2 which makes it a quadratic equation.
Ques. What is a math equation? (2 Marks)
Ans. A math equation is considered as the mathematical expression with an 'equal sign between two algebraic expressions that have equal values.
For instance, 4a + 5 = 15 is a math equation. It has 4a + 5 on the left-hand side and 15 on the right-hand side. The operator used here is the addition (+).
Ques. Give a few examples of math equations. (3 Marks)
Ans. Given below are a few examples of math equations:
Example 1: x - 5 = 6
x = 6 + 5
x = 11
In this equation, x is a variable and 5 is the constant.
Example 2: 4c - 5 = 15
4c = 15 + 5
4c = 20
c = 20/4 (On dividing)
c = 5
In this way, this type of equation is solved.
Ques. What are the steps to solve radical equations? (3 Marks)
Ans. The process of solving radical equations almost always involves rearranging the radical equations into quadratic equations, then solving the quadratic equations. As such, knowledge of how to manipulate polynomials algebraically and solve a variety of quadratic equations is essential to successfully solve radical equations.
Ques. What are Exponential Equations? (3 Marks)
Ans. In the math equation, an equation that contains the variables in place of exponents is an exponential equation. By using the property, an exponential equation can be solved. We know that the exponent of a number (base) indicates the number of times the number (base) is multiplied. When the power is a variable and if it is a part of an equation, then It is called an exponential equation.
Ques. What are some points to be kept in mind while solving equations? (3 Marks)
Ans. Few things to be kept in mind while solving the equation.
- To be focused while reading out the question. It should be read at least 2 times to know and understand the type of equation.
- To clearly see the exponents and their base while solving the exponential equation.
- To make an early structure of the equation that is to be derived again to solve it to the next step.
- To see the numerators and denominators properly if the equation is given in the fractional form.
- To recheck the values of the variables while going for the final answer, The LHS must be equal to RHS.
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