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AQA GCSE · Question 10.1 · Algebra
Represent -2 < x < 4 on the number line.
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.
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