Question

If \[x + 1 = {\text{ 23}}\], calculate the value of \[3x + 3\] ?

Answer 1

Hint: To solve this question , we are given the expression \[x + 1 = {\text{ 23}}\]. There is one term in our expression , for which we can perform the calculations. We can apply the concept of “ equivalent ” which refers to the equal to in quantity. And when we merge the word “ equation “ with this then the complete term is made up of “ equivalent equation ”. This actually means that the equivalent equations are the equations that may have the same solutions. To find the solution of algebra equivalent equations makes it easier. We will solve for x and then substitute the value of x in the other equation to calculate the value of \[3x + 3\].

Complete step-by-step solution:
We need to solve this for ‘ x ‘ for the equation. the value of x comes to be identical for both the equations then the above two equations are said to be equivalent.
Solving for first equation - \[x + 1 = {\text{ 23}}\]
Now , we are going to subtract both sides by the same number ‘ 1 ‘(one of the properties of the equivalent equation)
$x + 1 - 1 = {\text{ 23 - 1}}$
$x = 22$
The value for x comes to be 22.
Solving for second equation - \[3x + 3\]
Now , we are going to substitute the value of x in this equation to calculate its value..
$
   = 3x + 3 \\
   = 3 \times 22 + 3 \\
   = 66 + 3 \\
   = 69 \\
 $
The value of x is equal to 22 and when substituted with the same number 22 , we get the value of the expression \[3x + 3\] as 69.

Hence the correct answer is ‘69’.

Note: In equivalent equations which have identical solutions we can perform addition or subtraction by the same number to both L.H.S. and R.H.S. of an equation.
i) In equivalent equations which have identical solutions we can perform multiplication or division by the same non-zero number both L.H.S. and R.H.S. of an equation.
ii) In an equivalent equation which has an identical solution we can take the same odd square root to both L.H.S. and R.H.S. of an equation.
iii) In equivalent equations which have identical solutions we can raise the same odd power to both L.H.S. and R.H.S. of an equation. Be careful while substituting the value of x in the other equation.