Question

How do you solve $50\ge 15x$?

Answer 1

Hint: In this problem we need to solve the given expression that means we need to calculate the values or range of $x$ such that the given expression for all $x$ values is satisfied. We can observe that the given expression has a constant value and a variable with coefficient. So first we will consider both of them and factor each value. Now substitute those factored values in the given expression and observe the common factors that we have on both sides. To get the required result divide the obtained expression with the common factors we have and simplify the expression to get the required result.

Complete step by step answer:
Given that, $50\ge 15x$.
In the above expression we have $50$ as constant and $15$ is the coefficient of the variable $x$.
Considering the constant value which is $50$.
We can prime factorise the value $50$ as $50=2\times 5\times 5$.
Considering the coefficient which is $15$.
We can prime factorise the value $15$ as $15=3\times 5$.
Substituting these values in the given expression, then we will get
$\begin{align}
  & \Rightarrow 50\ge 15x \\
 & \Rightarrow 2\times 5\times 5\ge 3\times 5\times x \\
\end{align}$
On both sides we have the common factor $5$. So, cancelling one $5$ on both sides of the above expression, then we will get
$\Rightarrow 2\times 5\ge 3\times x$
For solving $x$ value we are going to divide the above equation with $3$ on both sides of the above equation, then we will have
$\begin{align}
  & \Rightarrow \dfrac{2\times 5}{3}\ge \dfrac{3\times x}{3} \\
 & \Rightarrow \dfrac{10}{3}\ge x \\
\end{align}$
Flipping the above expression, then we will get
$\Rightarrow x\le \dfrac{10}{3}$

Hence the solution for the given expression $50\ge 15x$ is $x\le \dfrac{10}{3}$.

Note: For this problem we can directly find the solution without considering the prime factors of the various values which are in the given expression. We can simply divide the given expression with coefficient of the $x$ which is $15$ on both sides and simplify the expression to get the result.
Dividing the given expression with $15$ on both sides, then we will get
$\begin{align}
  & \Rightarrow \dfrac{50}{15}\ge \dfrac{15x}{15} \\
 & \Rightarrow \dfrac{10}{3}\ge x \\
 & \Rightarrow x\le \dfrac{10}{3} \\
\end{align}$
From both the methods we got the same result.