Linear Inequalities
The solution to algebraic inequalities consists of a range (or ranges) of numbers. The solution to linear inequalities will be of the form x < a, x ≤ a, x > a, or x ≥ a, where a is a number. The inequality x < a means all numbers smaller than a but not including a; x ≤ a means all numbers smaller than a including a itself. Similarly the inequality x > a means all numbers larger than a but not a itself, and x ≥ a means all numbers larger than a including a itself.
The solutions to some algebra and calculus
problems are inequalities. Sometimes you will be asked to shade these
inequalities on the real number line and sometimes you will be asked to give
your solution in interval notation. Every interval on the number line can be
represented by an inequality and every inequality is represented by an interval
on the number line. First we will represent inequalities by shaded regions on the
number line. Later we will represent inequalities by intervals.
The inequality x < a is represented on
the number line by shading to the left of the number a with an open dot at a.
A closed dot
is used for x ≤ a.
Shade to the
right of a for x > a.
Use a closed
dot for x ≥ a.
Examples
Practice
Shade the
region on the number line.
Solutions
“Sumber Informasi”
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