Easy1 markStructured
AlgebraInequalitiesNumber LineAlgebra

AQA GCSE · Question 10.1 · Algebra

-5 -4 -3 -2 -1 0 1 2 3 4 5 x

Represent -2 < x < 4 on the number line.

How to approach this question

The inequality -2 < x < 4 means that x is greater than -2 and less than 4. 1. Because the symbols are < (and not ≤), x cannot be equal to -2 or 4. We represent this on the number line with open (unfilled) circles at -2 and 4. 2. Because x is between these two values, we draw a line connecting the two circles.

Full Answer

An open circle (o) is placed at -2. An open circle (o) is placed at 4. A line segment is drawn connecting the two circles.
This question asks to represent a double inequality on a number line. The inequality is -2 < x < 4. This can be read as two separate inequalities: x > -2 and x < 4. - The `x > -2` part means x is any number larger than -2. On a number line, we indicate this with an open circle at -2 (because it's not "greater than or equal to") and shading to the right. - The `x < 4` part means x is any number smaller than 4. We indicate this with an open circle at 4 and shading to the left. - Combining them means we want the numbers that satisfy both conditions, which is the region between -2 and 4. So, we draw an open circle at -2, an open circle at 4, and connect them with a solid line.

Common mistakes

✗ Using filled (closed) circles instead of open circles. This would represent -2 ≤ x ≤ 4. ✗ Shading in the wrong direction (outside the interval). ✗ Not connecting the two circles with a line.

Practice the full AQA GCSE Maths Higher Tier Paper 1 Non-Calculator

32 questions · hints · full answers · grading

More questions from this exam