Question

How do you solve 8-2x is greater than or equal to $-4$ ?

Answer 1

At first, we read the entire sentence and try to understand what it means. After that, we have to find the keywords in it, such as “greater than” over here and look for what symbols that we have for such keywords, like $\ge$ . Having done all of these, we have the mathematical expression at our hand which can be easily solved.

Complete step-by-step solution:
The most important thing in mathematics, or rather the entire science domain is the conversion of words into numbers or expressions. It is the link that keeps the various thoughts and various equations connected, the thoughts being in words and the representation of the thoughts being in mathematical or scientific expressions.
The given sentence or phrase that we need to convert in this problem is “ $8-2x$ is greater than or equal to $-4$ ”. Though, $8-2x$ and $-4$ are mathematical expressions and numbers, the rest of the sentence contains words which we need to convert into some symbols. Now, it is said that $8-2x$ is greater than or equal to. The use of “or” indicates that $8-2x$ is either greater than or it is equal to $-4$ or both. But, being greater than and equal to cannot occur simultaneously, so it will be any one at a time. We have a dedicated symbol for the phrase “greater than or equal to” which is $\ge$ . Thus, the entire sentence gets reduced to,
$\Rightarrow 8-2x\ge -4$
This can now be solved easily using our mathematical knowledge as,
$\begin{aligned} & \Rightarrow -2x\ge -12 \\\ & \Rightarrow x\le 6 \\\ \end{aligned}$
Therefore, we can conclude that the solution of the problem is $x\le 6$ .

Note: The conversion of words into mathematical expression is the most important thing over here. Students can commit mistakes in translation by overlooking some words such as “than” which if done can lead to difference. Special care must be taken while multiplying negative signs to both sides of an inequality. Also, not to mention, the signs in the expression should be handled with care.