Math CentralQuandaries & Queries


Question from LANELL, a student:

this is a problem to solve: 1/3 + 2/7 >=x/21 -- part of the answer is (-oo)
not exactly that similar--it is on a calculator as a symbol- sure you know what it is I am talking about- the x will be a number

Hi Lanell,

I'm not going to solve your problem but I will show you how to solve a very similar problem.

Solve the inequality $\frac25 - \frac34 \geq \frac{7x}{20}.$

I would first multiply both sides by $20$ to clear the fractions and get $8 - 15 \geq 7x.$ simplification gives $-7 \geq 7x$ or $-1 \geq x.$ I prefer to read this from right to left to get $x \leq -1.$

The question now is how to write the answer. You might say the answer is

the set of all numbers $x$ so that $x$ is less than or equal to $-1.$

You might use set notation

$\{x \;|\; x \leq -1 \}.$

Sometimes people imagine a fictitious number, minus infinity (written $-\infty$) at the far left end of the number line and writee the answer as

the set of all numbers $x$ so that $- \infty < x \leq -1.$

Sometimes this is written as an interval

the solution set is $(-\infty, -1].$

I hope this helps,

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