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Double inequalities

A double inequality says that an expression lies between two numbers. You do the same operation on all three parts. If you subtract a number, you do it in the left, middle and right part. If you divide by a positive number, you keep both signs. In the end x should stand alone in the middle, with the smaller value on the left. Read the solution as an interval.

Symbols

Example

$-1 < 2x + 1 < 5$. Subtract 1: $-2 < 2x < 4$.

Divide by 2: $-1 < x < 2$. The boundaries are $\dfrac{-1 - 1}{2} = -1$ and $\dfrac{5 - 1}{2} = 2$.

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Part of Mathematics S1: Inequalities and sign charts.