# Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the **Number system.** Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero.

**What is an Equation?**

An **equation** is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign.

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**For example:** In equation **3x+2 = 5**, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign.

There are mainly 3 types of equations:

- Linear Equation
- Quadratic Equation
- Polynomial Equation

Here, we will study the Linear equations.

**Linear equations in one variable** are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2=5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

- 4x = 8
- 5x + 10 = -20
- 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

- The numbers ‘a’ and ‘b’ are real.
- Neither ‘a’ nor ‘b’ are equal to zero.

**Solving Linear Equations in One Variable**

The steps for solving an equation with only one variable are as follows:

**Step 1:** If there are any fractions, use LCM to remove them.

**Step 2:** Both sides of the equation should be simplified.

**Step 3:** Remove the variable from the equation.

**Step 4:** Make sure your response is correct.

**Problem Statement:** Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

**Solution:**

Let the three consecutive odd integers are num-2, num, num+2, where num is an odd integer.

According to the problem statement, Three times the first of three consecutive odd integers is 3 more than twice the third i.e.

3*(num-2) = 2*(num+2) + 3

To get the numbers, we have to solve this linear equation i.e.

Now, solving the equation using above steps:

3*(num-2) = 2*(num+2) + 3

3*num – 6 = 2*num + 4 + 3

3*num – 6 = 2*num + 7

3*num -2*num = 7 + 6

num = 13

So, the value of num is **13** i.e. the second integer.

First integer is num – 2 i.e. 13 – 2 = **11.**

Third integer is num + 2 i.e. 13 + 2 = **15. **

So, 11, 13, and 15 are the three consecutive odd integers.

**Similar Questions**

**Problem 1: Two times the first number is equal to three times the** **second number and the sum of both numbers is 5. Find the numbers.**

**Solution:** Let the two numbers are num1 and num2.

According to the problem statement,

Two times the first number is equal to three times of second number i.e.

2*num1 = 3*num2 (eq -1)

Also, Sum of both numbers is 5 i.e.

num1 + num2 = 5 (eq -2)

To get the numbers, we have to solve these equations i.e.

Now, solving the equation using the above steps:

Taking eq-2 :

2*num1 = 3*num2num1 = (3*num2) / 2Taking eq-1 i.e.

num1 + num2 = 5

Now put the result of 1st equation i.e. num1 = (3*num2)/2 in 2nd equation i.e.(3*num2)/2 + num2 = 5

Taking LCM

(3*num2 + 2*num2 ) / 2 = 5

3*num2 +2*num2 = 5 * 2

5*num2 = 10

i.e. num2 = 10/5 i.e.2So, the value of num2 is

2and using this the value of num1 is 5-num2 = 5-2 =3.

**Problem 2: The sum of four consecutive numbers is 18, find the numbers.**

**Solution: **

Let the four consecutive numbers are x, x+1, x+2, x+3 respectively.

So, according to the problem statement:

x + x+1 + x+2 + x+3 = 18

Using this equation we can get the value of x i.e. the first number4x + 6 = 184x = 18-64x = 12x = 12/4x = 3

So, the numbers should be 3, 4, 5, and 6.