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Q54.

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Found in: Page 11

Precalculus Mathematics for Calculus

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 $\left[1,2\right]$.

See the step by step solution

Step 1. Apply the concept of interval and inequality.

If $a, 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

Step 2. Express in terms of inequality.

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:

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

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

Step 3. Graph the interval.

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: