Question

Two less than 4 times a number is the same as the number plus 34. Find the number?

Answer 1

Hint: We first assume the number as $x$ and find the algebraic expression of the given conditions separately where two less than 4 times the number is the same as the number plus 34. We solve the equation and find the value of the variable.

Complete step-by-step solution:
We assume the number to be $x$.
It is given that two less than 4 times a number is the same as the number plus 34.
We separately form the algebraic expression of the given conditions.
We first take the Two less than 4 times the number $x$.
This gives $4x-2$.
Now we take the number $x$ plus 34 which is equal to $x+34$.
As they are equal, we get $4x-2=x+34$.
We now solve the expression to get
$\begin{array}{rl}& 4x-2=x+34\\ & \Rightarrow 4x-x=34+2\\ & \Rightarrow 3x=36\\ & \Rightarrow x={\displaystyle \frac{36}{3}}=12\end{array}$
The number is 12.

Note: We need to be careful about the back calculation process to verify the solution.
From Two less than 4 times the number 12, we get $4\times 12-2=48-2=46$.
From the number $x$ plus 34, we get $x+34=12+34=46$.
The condition satisfies the answer and also verifies it.