Question

An elevator can hold $2,800$ pounds or less. How do you write and solve an inequality that describes how much more weight the elevator can hold if it is currently holding $2,375$ pounds?

Answer 1

To solve the above question will use the inequality. In mathematics, inequalities are used to compare the relative size of values. The can be used to compare integers, variables, and various algebraic expressions. It is a statement in which one quantity is specifically less than or other is greater. It describes a relation between two different values. Inequalities are particularly useful for solving problems involving minimum or maximum possible values.

Complete step-by-step solution:
The elevator can hold $2,800$pounds or less, it means we have to find an equality which is always less or equal to $2,800$pounds.
Let $x$ be the additional weight we need to calculate and given that currently the elevator is holding $2,375$pounds, it means we have to find that of $x$ so by adding it in $2,375$the weight could not exceed $2,800$.
Now by writing all these values in equality we get,
$\Rightarrow x+2375\le 2800$
To solve this inequality first we will subtract $2,375$from both side, we get
$\Rightarrow x+2375-2375\le 2800-2375$
The left side get cancel out and in right side we will subtract $2,375$from$2,800$then, we get
$\Rightarrow x\le 425$
Hence, the value of additional weight can be less than or equal to $425$. Beyond this value the elevator becomes unable to hold the weight.

Note: In these types of questions we can go wrong by putting wrong inequality. So before doing a solution first carefully read and understand which equality is required. In mathematics we have many inequalities like$\left( \le ,\ge ,\ll ,\gg \right)$ and many more.