Number line & inequalities

<p class="paragraph-header">Translating the conditions</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>Words</strong></th><th style="text-align: center; --cell-justify: center"><strong>Mathematical meaning</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">At most; no more than</td><td style="text-align: center; --cell-justify: center">\(\leq\)</td></tr><tr><td style="text-align: center; --cell-justify: center">At least; no less than</td><td style="text-align: center; --cell-justify: center">\(\geq\)</td></tr><tr><td style="text-align: center; --cell-justify: center">More than; fewer than</td><td style="text-align: center; --cell-justify: center">\(&gt;\); \(&lt;\)</td></tr></tbody></table></div></div>
<p>Define the variable and its unit. Form an inequality for each condition, then combine the restrictions. Counts of people, tickets or packs must be non-negative integers.</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>Algebraic bound for a count</strong></th><th style="text-align: center; --cell-justify: center"><strong>Consequence</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(n\leq12.6\)</td><td style="text-align: center; --cell-justify: center">Greatest possible integer: 12</td></tr><tr><td style="text-align: center; --cell-justify: center">\(n\geq12.6\)</td><td style="text-align: center; --cell-justify: center">Least possible integer: 13</td></tr><tr><td style="text-align: center; --cell-justify: center">\(n&lt;12\)</td><td style="text-align: center; --cell-justify: center">Greatest possible integer: 11</td></tr></tbody></table></div></div>
<p>Do not round a count to the nearest integer automatically. Decide whether the question asks for a greatest feasible count or a least required count, then check it in the original situation.</p>
<p>An equation can connect two quantities. Express one in terms of the other, substitute into the stated bounds and retain exact fractions until the integer choices have been identified.</p>

Define the variable and its unit. Form an inequality for each condition, then combine the restrictions. Counts of people, tickets or packs must be non-negative integers.

Do not round a count to the nearest integer automatically. Decide whether the question asks for a greatest feasible count or a least required count, then check it in the original situation.

An equation can connect two quantities. Express one in terms of the other, substitute into the stated bounds and retain exact fractions until the integer choices have been identified.

Inequalities in context

Inequalities in context

Words	Mathematical meaning
At most; no more than	\(\leq\)
At least; no less than	\(\geq\)
More than; fewer than	\(>\); \(<\)

Algebraic bound for a count	Consequence
\(n\leq12.6\)	Greatest possible integer: 12
\(n\geq12.6\)	Least possible integer: 13
\(n<12\)	Greatest possible integer: 11