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Exercises Equations and inequalities

Example 2.66 from Elementary Algebra, 2.7 Solve Linear Inequalities

Solve Linear Inequalities: example 2.66

Graph on the number line:

ⓐ $x \leq 1$ ⓑ $x < 5$ ⓒ $−1$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ $x \leq 1$
  This means all numbers less than or equal to 1. We shade in all the numbers on the number line to the left of 1 and put a bracket at $x = 1$ to show that it is included.
2. ⓑ $x < 5$
  This means all numbers less than 5, but not including 5. We shade in all the numbers on the number line to the left of 5 and put a parenthesis at $x = 5$ to show it is not included.
3. ⓒ $x > - 1$
  This means all numbers greater than $−1$ , but not including $−1$ . We shade in all the numbers on the number line to the right of $−1$ , then put a parenthesis at $x = −1$ to show it is not included.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph on the number line: ⓐ $x \leq - 1$ ⓑ $x > 2$ ⓒ $x < 3$

How did it go?

PreviousSolve a Formula for a Specific Variable: example 2.65 Next Solve Linear Inequalities: example 2.67

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 2.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.