Inequality on the Number Line

Algebra 1 · Axiom Academy

An inequality isn't one answer — it's a whole stretch of the number line. See which numbers make it true, and what the little circle is really telling you. One inequality, a whole region of answers Solving x = 3 gives you a single number. But is true for 3.1 , for 4 , for a million — an entire run of the number line. The number line is where that whole solution lives, so this is where we'll learn to read it. Watch the boundary at 3 as the symbol changes: the circle fills in or hollows out, and the shaded ray flips to whichever side makes the statement true. Two things ride on the symbol — which way you shade, and whether the boundary itself counts. An open circle leaves the boundary out; a closed circle pulls it in. The shaded side is every number that makes the inequality true. Test a number: is it in the solution? Take the inequality and drag the blue dot to try different values of x . Every number you land on is either in the solution or it isn't — the verdict updates as you move. Watch where the "true" values bunch up. Every value above 3 works; nothing at 3 or below does. That whole run of true values is the solution set. Same boundary at 3 , four different symbols. Tap each one and watch two things respond at once: the circle (open means 3 is left out, closed means it's pulled in) and the direction of the shaded ray. The "or-equal-to" line under the symbol is exactly what fills the circle.

This is the written version of the interactive lesson above. See the full Algebra 1 course.