Question

Find the number which when multiplied by 7 is increased by 78.

Answer 1

Hint:An algebraic equation involves the equality variables. It says that the value on one side is equal to the expression on the other side. A linear equation can have linear expression on both sides. Like the numbers, variables can be transposed from one side to the other. Sometimes the expressions forming equations have to be simplified before solving.The common variable used is ‘x’ but any variable can be used.

Complete step by step answer:
Let the required number be denoted as ‘ \[x\] ’. According to the question, when \[x\] is multiplied by 7, that is, \[x\times 7\].
Then \[x\] is increased by 78, that is, \[x+78\]
Both the expressions are equal so we can write
\[x\times 7=x+78\]
The above equation can be written as
\[7x=x+78\]
Subtracting \[x\] from both sides we get
\[7x-x=x+78-x\]
Solving further we get
\[6x=78\]
Dividing by 6 on both sides we get
\[\dfrac{6x}{6}=\dfrac{78}{6}\]
Solving further we get
\[\therefore x=13\]

Therefore, the required number is 13.

To check the answer we can solve the LHS and RHS separately by substituting\[x=13\].
LHS:
\[7x=7\times 13\]
\[\Rightarrow x= 91\]
RHS:
\[x+78=13+78\]
\[\Rightarrow x=91\]
Hence LHS is equal to RHS and the answer is verified.

Note:The expression on the left side of the equality sign is the LHS (Left Hand Side) and the expression on the right side of the equality sign is the RHS (Right Hand Side). To find the solution of the equation we have assumed the two sides of the equation are balanced.Then we perform the same mathematical operations on both sides so that the balance is maintained and few such steps lead us to the final solution.