Number line & inequalities

<p class="paragraph-header">Describing a set of values</p>
<p>An equation may identify a value. An inequality describes all values that satisfy a comparison. Unless a question specifies integers or a context restricts the variable, consider real values.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Symbol</strong></th><th style="text-align: center; --cell-justify: center"><strong>Meaning</strong></th><th style="text-align: center; --cell-justify: center"><strong>Endpoint</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(&lt;\) or \(&gt;\)</td><td style="text-align: center; --cell-justify: center">Strictly less than or greater than</td><td style="text-align: center; --cell-justify: center">Open circle: endpoint excluded</td></tr><tr><td style="text-align: center; --cell-justify: center">\(\leq\) or \(\geq\)</td><td style="text-align: center; --cell-justify: center">Less than or equal to; greater than or equal to</td><td style="text-align: center; --cell-justify: center">Filled circle: endpoint included</td></tr></tbody></table></div></div>
<p>The statement \(-2\leq x&lt;5\) means that both&nbsp;\(x\geq-2\) and \(x&lt;5\) hold. The segment below represents every real value between these boundaries, including \(-2\) but excluding \(5\).</p>
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<p>If&nbsp;\(x\) must be an integer, select only the integers in the interval. Keep boundary values exact: replacing a fraction by a rounded decimal can change the solution set.</p>

An equation may identify a value. An inequality describes all values that satisfy a comparison. Unless a question specifies integers or a context restricts the variable, consider real values.

The statement \(-2\leq x<5\) means that both \(x\geq-2\) and \(x<5\) hold. The segment below represents every real value between these boundaries, including \(-2\) but excluding \(5\).

If \(x\) must be an integer, select only the integers in the interval. Keep boundary values exact: replacing a fraction by a rounded decimal can change the solution set.

Inequality notation and number lines

Inequality notation and number lines

Symbol	Meaning	Endpoint
\(<\) or \(>\)	Strictly less than or greater than	Open circle: endpoint excluded
\(\leq\) or \(\geq\)	Less than or equal to; greater than or equal to	Filled circle: endpoint included