Question

Four less than half a number is equal to $37$ less than twice the number. How to translate the sentence into an equation and solve the equation?

Answer 1

Hint: In this problem we need to find the equation and solve the equation according to the given data. For this type of problem, we need to know about how the terms are used as symbols. In the given data we have two parts. The first part is writing the equation for the given data. The second part is finding the solution for the given data. So first we will write the equation according to the given data by using the appropriate symbols for the given terms. After getting the equation, we will solve the equation by using algebraic or arithmetic formulas.

Complete step-by-step solution:
Given that, Four less than half a number is equal to $37$ less than twice the number.
Let us assume the number as $x$.
From the given statements
Half a number means $\dfrac{x}{2}$.
Four less than half a number means $\dfrac{x}{2}-4$.
Twice of a number means $2x$.
$37$ less than twice the number means $2x-37$.
Now the mathematical form of the given statement Four less than half a number is equal to $37$ less than twice the number is given by
$\dfrac{x}{2}-4=2x-37$.
Hence the required equation is $\dfrac{x}{2}-4=2x-37$.
Solving the above obtained equation.
Rearranging the terms in the above equation, so the all the variables are at one side and constants are at one side, then we will get
$2x-\dfrac{x}{2}=37-4$
Simplifying the above equation, then we will get
$\begin{align}
  & 2x-0.5x=37-4 \\
 & \Rightarrow 1.5x=33 \\
 & \Rightarrow x=\dfrac{33}{1.5} \\
 & \Rightarrow x=22 \\
\end{align}$
Hence the solution of the equation is $x=22$.

Note: We can also check whether the obtained solution is correct or not by checking the equation’s value at $x=22$. Substituting $x=22$ in the equation, then we will get
$\begin{align}
  & \dfrac{x}{2}-4=2x-37 \\
 & \Rightarrow \dfrac{22}{2}-4=2\left( 22 \right)-37 \\
 & \Rightarrow 11-4=44-37 \\
 & \Rightarrow 7=7 \\
 & \Rightarrow LHS=RHS \\
\end{align}$