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Q54.

Expert-verifiedFound in: Page 11

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

Express the inequality in interval notation, and then graph the corresponding interval.

$1\le x\le 2$

The inequality form of the given interval $\left[1,2\right]$.

If $a<b$, then the open interval from *a* to *b* consists of all numbers between *a* and *b* and is denoted by $\left(a,b\right)$. The closed interval from *a* to *b* includes the endpoints and is denoted by $\left[a,b\right]$.

Using the set-builder form, we can write the intervals as inequality:

$\left(a,b\right)=\left\{x|a<x<b\right\}\phantom{\rule{0ex}{0ex}}\left[a,b\right]=\left\{x|a\le x\le b\right\}$

Given inequality is $1\le x\le 2$

This includes all the numbers between 1 and 2, including both.

Using set-builder form to express the inequality:

$\left\{x\right|1\le x\le 2\}$

So, the interval is given by $\left[1,2\right]$

From step 2, we have $\left[1,2\right]$

This represents all the numbers between 1 and 2, including both.

Since 1 and 2 are included in the interval, they will be represented by closed circles.

So, the graph will be:

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