# Math Equations

Math equations allow you to solve an equation or a system of equations. The equation is a statement that holds the equality of two expressions. Most of the cases you can find the exact solutions for the given math equations. But most of the times it is not possible to get the exact solution but can find the approximate solutions that will match the accuracy of the exact solution. It deals with the special commands involving quadratic math equations.

An equation defines a mathematical sentence that states that two algebraic expressions must be equal in nature. Consider the example,

Case 1: xy = yx

Case 2: a(x+y)=ax+ay

Case 3: a^{2} -1 = (a+1)(a-1)

When you define the values for variables, the values on both sides remains the same. Assume that x = 2 and y = 3, we get 2 x 3 = 3 x 2 gives 6 = 6. The numbers that are specified to the variables to maintain the equality of an equation are the replacement numbers for the variables. When the variable is replaced by a specific number and it maintains the equality of an equation, then the specific number is called a solution of an equation. From the above example, we can say that 2 and 3 are the solutions of an equation. The solutions obtained through an equation is called the solution set of the given math equations. Therefore the solution set is defined by { 2, 3 }. In the replacement set, an identity equation is always satisfied by all the numbers that are present in the sets.For example x y=y x = 2 x 3 = 3 x 2. In a conditional equation, it is satisfied by certain numbers of the replacement sets. Consider a math equation 2x=6, here 3 is the only solution of an equation. If you use the number other than 3, it fails to meet the condition criteria for a given equation.

## Different Types of Equations

Some of the lists of math equations involved in algebra are

- Quadratic Equation
- Linear Equation
- Radical Equation
- Exponential Equation
- Rational Equation

**Linear Equations**

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 ,\(m\neq 0\)

Where m is the slope

C is the point on which it cut y-axis

Example : Linear equation with one variable : 10x – 80 = 0

Linear equations with two variables : 9x + 6y – 82 =0

**Quadratic Equations**

The quadratic equation is a second-order equation in which any one of the variable contains an exponent of 2. The general form of the quadratic equation is

ax^{2}+bx+c = 0, \(a\neq 0\)

Example : 5x^{2} – 5y -35=0

Here a = 5, b=-5 and c=-35

**Radical Equations**

In a radical equation, a variable is lying inside a square root symbol or you can say that the maximum exponent on a variable is ½

Example : \(\sqrt{a}+10 = 26\)

**Exponential Equations**

In this math equations, it contains the variables in place of exponents. By using the property, an exponential equation can be solved. \(a^{x}=a^{y}\Rightarrow x=y\)

Example : 8^{x} = 32

The above equation is equivalent to 8^{x} = 8^{4.}

**Rational Equations**

A rational math equations involves the rational expressions

Example : \(\frac{y}{2}=\frac{y+2}{4}\)

### Math Equations Example

**Question 1 :**

Find the solution for the given equation and check the answer

4x – 7 (2-x) = 3x + 2

**Solution :**

Given : 4x – 7 (2-x) = 3x + 2

Simplify the left side of equation within the bracket

4x – 14 + 7x = 3x + 2

11x – 14 = 3x + 2

Now, bring all the ‘x’ terms on one side and constant term on other side

11x-3x = 14 + 2

8x = 16

X = 16/8

X = 2

Therefore, the solution for the given equation 4x – 7 (2-x) = 3x + 2 is 2

**Verification :**

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.

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