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Find two consecutive odd integers such that twice the greater is 17 more than the lesser

  • Last Updated : 29 Oct, 2021

Algebra is a part of mathematics in which we deal with numerals and variables. When we talk about numbers, we are pretty sure that it will be some fixed value but when we talk about variables we can not say much about the number. The value of the variable is not fixed. It can take any value. We usually represent algebra with the help of alphabetical letters. For example, if we have to represent an equation of quotient, dividend, remainder, and divisor then we can represent it like: 

D = d × q + r

Here, D represents dividend, ‘d’ represents divisor, q represents quotient, and r represents remainder.

According to the condition given in the question, we can find out the unknowns. Further in this article, we will discuss, how to form an algebraic equation and how to get the exact answer.

Algebraic Expressions

An algebraic expression is the combination of numerals and variables by fundamental arithmetic operators. For example, we have two numerals 3 and 5, and one variable x then we can form an algebraic expression 5x + 3.

On the basis of the number of terms, an algebraic expression can be categorized into the following types.

  • Monomial; In the number of terms in an algebraic expression is one then that algebraic expression is termed as the monomial. Example: 5x , 6y, etc.
  • Binomial: If the number of terms in an algebraic expression is two the algebraic expression is termed binomial algebraic expression. Example: 6x + 3, 5y + 3, etc.
  • Trinomial: If the number of terms in an algebraic expression is three then the algebraic expression is termed as the trinomial. Example: 5x + 6y + 9, 8x + 9y + 5, etc.
  • Polynomial: If the number of terms in an algebraic expression is one or more than one then that expression is termed as the polynomial.

Algebraic Equation

When an algebraic expression is equal to some other algebraic expression or values then we term it as ‘algebraic equation’. Or in another word we can say when an ‘=’ sign is introduced between an algebraic expression and separate it in two different parts, i.e. Left Hand Side (LHS) and Right Hand Side (RHS). 

To get the solution of an algebraic equation, solve the expression on the left-hand side and the expression on the right-hand side. Equate the left-hand side and right-hand side and get the value of the variable.

Step to solve an algebraic equation:

Step 1: Form the equation on the basis of the information given in the question.

Step 2: Suppose unknowns as the letter of the alphabet. We term them as variables. 

Step 3: Now equate the equation.

Step 4: Add or subtract all the like terms of the variable.



Step 5: If a number is positive on one side and we transfer it to the other side of the equal sign then it gets changed into the negative sign. Similarly, negative changes to positive multiplied changes to divide, and divide changes to multiply. 

Step 6: By using the above rule transfer all variables on one side and numerals on the other side and get the value of the unknown.

Find two consecutive odd integers such that twice the greater is 17 more than the lesser

Solution: 

Let the first integer be x.

The other consecutive odd integer will be x + 2.

Here, we can clearly observe that x + 2 will be the greater integer than x.

Now according to the question, twice times the greater is 17 more than the lesser.

⇒ 2 × (x+2) = x +17

Solve the above equation.

⇒ 2x + 4 = x + 17



⇒ 2x – x = 17 – 4

⇒ x = 13

So, the first integer is 13 and the next integer is 13 + 2, i.e. 15.

Similar Questions

Question 1: If the sum of two consecutive odd integers is 32. Then find the integers.

Solution:

Let the first integer be x.

The other consecutive odd integer will be x + 2.

According to the question, the sum of these two is 32.

⇒ x + (x + 2) = 32

⇒ x + x + 2 = 32

⇒ 2x + 2 = 32

⇒ 2x = 32 – 2

⇒ 2x = 30

⇒ x = 30 ÷ 2

⇒ x = 15

The first integer is 15 and next integer is 17.

Question 2: Find two consecutive odd integers such that thrice the first is 6 more than the second.

Solution:

Let the first integer be x.

The next even integer will be x + 2.

According to the question, thrice the first is 6 more than the second.

⇒ 3 × x = (x+2) + 6

⇒ 3x = x + 2 + 6

⇒ 3x – x = 8

⇒ 2x = 8

⇒ x = 8 ÷ 2 

⇒ x = 4

So, the first integer is 4 and next integer is 6.

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