Question

How do you write the inequality for “Josephine sleeps more than 7 hours each night”?

Answer 1

We first try to make the given written statement in its mathematical form. We assume the variable $x$ to as the required number. Then we form the relation. As the exact value is not mentioned, we form the inequality. We get the value of the variable as the solution. We apply the binary operation of addition. To get the value of b, we need to add the value of 7.

Complete step by step solution:
The given statement about the required number of hours is that Josephine sleeps more than 7 hours each night. We take the number of hours as $x$.
As no exact number of sleeping hours for Josephine is mentioned, we only can form the inequality.
The expression is that $x$ has to be more than 7 and also it can not be equal to 7.
Therefore, the algebraic expression is $x>7$.
The possible values for $x$ can be anything greater than 7.
For equality purposes, if we assume $x=7+a$.
So, we subtract 7 from both sides. We get
$\begin{aligned} & x-7=7+a-7 \\\ & \Rightarrow a=x-7 \\\ \end{aligned}$
Therefore, the value of a is $x-7$.

Note: We need to remember that the inequality of $x\ge 7$ is also wrong as it also indicates the equality.The negation of the statement $x\le 7$ also indicates the same condition.