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Example: We can take any variable such as x, y, a, b, etc.Some examples of linear equations in one variable are, 2a + 3a = 20; 5x + x = 12, etc. The above equations are linear in one variable as they only have one variable and the highest degree of the variable is 1.

Solving Linear Equations in One Variable. A linear equation is an equation of a straight line, written in one variable. The only power of the variable is \(1\). Linear equations in one variable may take the form \(ax +b=0\) and are solved using basic algebraic operations. We begin by classifying linear equations in one variable as one of three ...

Example 3: Find the perimeter of the square whose side length x units is given in the form of an equation as 2x/3- 5/6=0 Solution: Given, the side-length of the square is 2x/3- 5/6=0. It is in the form of a linear equation in one variable which is x. First, we need to solve this equation to find the value of x. 2x/3- 5/6=0 2x/3- 5/6 + 5/6=0+ 5/6 (adding 5/6 on both the sides) 2x/3= 5/6 x = 5/6 ...

An equation in which the highest power of variable is one, is called a linear equation. For example: 4 x + 5 = 3 x + 1, 2 x + 3 y = 4 are linear equations. 2 x y + 1 = 3 → This is not an example of linear equation as the degree is two. 2.0 Linear equations In One Variable Definition. A linear equation which has only one variable is called a ...

3.0 Solving Linear Equation in One Variable: To Solve a linear equation in one variable, follow these few easy steps: Step 1: The first step is to identify that the equation is in the standard form of ax + b = 0. Step 2: Separation of variable Makes the variable on one side and constants on the other side with the help of arithmetic operations.

To solve a linear equation, it is a good idea to have an overall strategy that can be used to solve any linear equation. In the Example 5.12, we will give the steps of a general strategy for solving any linear equation. Simplifying each side of the equation as much as possible first makes the rest of the steps easier.

Linear equations in one variable are equations that can be expressed in the form ax + b = 0, where a and b are constants, and x is the variable. ... Example 2. Solve the equation (5x – 9 = 16). Solution: Add 9 to both sides to move the constant: 5x = 25 Divide both sides by 5: x = 5 The solution is (x = 5).

2.2 Linear Equations in One Variable. Topics covered in this section are: Solve equations in one variable algebraically. ... An identity equation is true for all values of the variable. Here is an example of an identity equation. $3x=2x+x$ The solution set consists of all values that make the equation true. For this equation, the solution set ...

Linear Equations and Their Solutions. An equation 129 is a statement indicating that two algebraic expressions are equal. A linear equation with one variable 130, \(x\), is an equation that can be written in the standard form \(ax + b = 0\) where \(a\) and \(b\) are real numbers and \(a ≠ 0\).For example \(3 x - 12 = 0\) A solution 131 to a linear equation is any value that can replace the ...

Solved algebra problems on linear equations in one variable are explained below with the detailed explanation. Let’s once again recall the methods of solving linear equations in one variable. ... Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. ...

What is Linear Equation in One Variable with Example? A linear equation of the form ax + b = 0 where x is the only variable is the standard form of a linear equation. Example: 5 x + 3 = 8 is a linear equation having a single variable x in it. The only solution for this equation is x = 1.

Solved Examples of Linear Equations in One Variable. The following are a few examples of questions that can come in examinations, related to Linear Equations in one variable. Example 1. The sum of the two numbers is 45 and their ratio is 2 : 3. Find the numbers. Solution: Let x be one of the numbers. Then, the other number is 45-x.

DEFINITION An equation is said to be linear if the variables in the equation all have exponents of 1 and if no term of the equation has more than one variable as a factor. The equation x+y-z = 1 is a linear equation in x,y, and z. The equation x^2+x-6 is not a linear equation. The equation 1x+xy = 9 is not a linear equation in x and y.

Solve linear equations in one variable using properties of equations. Construct a linear equation to solve applications. ... To solve a linear equation, it is a good idea to have an overall strategy that can be used to solve any linear equation. In the Example 5.12, we will give the steps of a general strategy for solving any linear equation. ...

Linear Equations in one variable can be defined as the equations with only one variable and a unique solution for that variable. An equation can have more solutions depending upon the number of variables. For example, a linear equation with two variables has two solutions. Examples of linear equations are: 4 + x = 5 (here x can only have a ...

Following are some examples of linear equation in one variable: (i) 2x = 8 (ii) 4y = 9 (iii) 3z = 7 (iv) 2x + 4= 7 (v) 81x + 45 =123. All the above mentioned examples have only one variable and are linear in nature. So, they are known as linear equation in one variable. The equation x 2 = 7x + 5 is not a linear equation because the highest ...

Learn more about Linear equations in one variables in detail with notes, formulas, properties, uses of Linear equations in one variables prepared by subject matter experts. ... Examples of Word Problems on Linear Equations in One Variable. Example: There are three numbers where the first number is twice the second, and the second is thrice the ...

The solution for an equation is a numerical value that, when inserted in the place of the unknown (or the variable), will render both members of the equation equal, that is, we will obtain a "true statement". In first degree equations with one unknown, there can only be one solution. Example: X − 1 = 5 X - 1 = 5 X − 1 = 5

More solved examples with detailed explanation on the word problems on linear equations. 6. Robert’s father is 4 times as old as Robert. After 5 years, father will be three times as old as Robert. Find their present ages. ... Problems on Linear Equations in One Variable.