This question tests writing inequalities like b ≤ c from constraints, understanding infinite solutions though contextually discrete, with inclusive symbols for maximums. Words to symbols: 'maximum' means ≤ (includes: b ≤ 6 up to 6), similar to 'at most'; infinite in theory but books are integers 0 to 6. Example: 'maximum 6 books' → b ≤ 6, solutions: 0,1,2,3,4,5,6 (finite integers, but conceptually infinite if fractions allowed, though not). Correct is b ≤ 6, matching choice C. Error: using <6 excluding 6, or >6 reversing, or claiming no infinite solutions when reals ≤6 are infinite. Writing: (1) identify 'maximum' as inclusive lesser, (2) to ≤, (3) b ≤ 6; graphing would be ● at 6 shaded left. Infinite solutions technically all reals ≤6, but context integers; mistakes: wrong symbol (≤ vs <), reversal.

This question tests writing inequalities like $w > c$ or $w < c$ from real-world constraints, understanding that they have infinitely many solutions, and representing them on number lines with proper boundary markers (● for included, ○ for excluded) and shading. Constraint words translate to symbols: 'at least' means ≥ (includes boundary, like $w \geq 36$ allows 36 or more), 'at most' means ≤ (includes), 'more than' means > (excludes), 'less than' means < (excludes); inequalities have infinite solutions unlike equations, and on a number line, use closed ● for ≥/≤, open ○ for >/<, shading right for greater and left for lesser. For example, 'at least 36' gives $w \geq 36$ with ● at 36 shaded right, infinite solutions. The correct number line is closed circle at 36 shaded right. A common error is open circle, excluding 36. For graphing: (1) mark 36, (2) closed ●, (3) shade right. Infinite solutions: all ≥36; mistakes include wrong circle or direction.

This question tests writing inequalities like a > c or a ≥ c from real-world constraints, understanding that inequalities have infinitely many solutions, and representing them on number lines with proper boundary markers such as closed circles (●) for inclusive or open circles (○) for exclusive, along with shading in the correct direction. Constraint words translate to symbols: 'at least' means ≥ which includes the boundary (a ≥ 13 means 13 or more), 'at most' means ≤ which includes it, 'more than' means > which excludes the boundary, and 'less than' means < which excludes it; inequalities have infinite solutions since they are satisfied by infinitely many numbers, unlike equations with finite solutions. For example, 'must be at least 13 years old' translates to a ≥ 13 where a is age, with solutions like 13, 14, 15, and infinitely many more, graphed as a number line with a closed circle at 13 and shading to the right (●======>). The correct inequality here is a ≥ 13, which includes 13 and all greater ages, matching choice B. A common error is using > instead of ≥ for 'at least,' excluding 13 incorrectly, or reversing to < or ≤, or misunderstanding infinite solutions by thinking only whole numbers count when actually all real numbers ≥13 satisfy it. To write this: (1) identify 'at least' as inclusive greater, (2) translate to ≥, (3) write a ≥ 13. For graphing: (1) draw number line, (2) mark 13, (3) use closed ● for ≥, (4) shade right for greater values; remember infinite solutions include all reals ≥13, and in context, ages like 13.5 would theoretically satisfy though practically ages are whole; mistakes include wrong symbol or circle type.

This question tests writing inequalities like g > c or g < c from real-world constraints, understanding that they have infinitely many solutions, and representing them on number lines with proper boundary markers (● for included, ○ for excluded) and shading. Constraint words translate to symbols: 'at least' means ≥ (includes), 'at most' means ≤ (includes), 'more than' means > (excludes boundary, like g > 2 allows above 2 but not 2), 'less than' means < (excludes); inequalities have infinite solutions unlike equations, and on a number line, use closed ● for ≥/≤, open ○ for >/<, shading right for greater and left for lesser. For example, 'more than 2' gives g > 2 with infinite solutions like 2.1, 3, .... The correct inequality is g > 2. A common error is using ≥, including 2 wrongly. To write: (1) identify 'more than' as >, (2) translate to g > 2. Infinite solutions: all >2; mistakes like confusing with at least (≥).

This question tests writing inequalities like x > c or x < c from real-world constraints, understanding that they have infinitely many solutions, and representing them on number lines with proper boundary markers (● for included, ○ for excluded) and shading. Constraint words translate to symbols: 'at least' means ≥ (includes boundary, like x ≥ 10 allows 10 or more), 'at most' means ≤ (includes, like x ≤ 50 allows 50 or less), 'more than' means > (excludes), 'less than' means < (excludes); inequalities have infinite solutions unlike equations, and on a number line, use closed ● for ≥/≤, open ○ for >/<, shading right for greater and left for lesser. For example, 'score more than 75' gives x > 75 with solutions like 76, 77, ... infinitely many, graphed as ○ at 75 shaded right. The correct inequality is x ≤ 50, as 'at most 50' includes up to 50. A common error is using < instead of ≤, excluding 50, or reversing to ≥ thinking of minimum. To write it: (1) identify 'at most' as ≤, (2) translate to x ≤ 50. Infinite solutions: all reals ≤ 50; mistakes include confusing at most with more than or wrong symbol.

This question tests writing inequalities like s > c from real-world constraints, recognizing infinitely many solutions, and the difference in symbols for exclusive vs inclusive boundaries. Constraint words to symbols: 'more than' → > (excludes boundary: s > 75 means above 75, not 75), 'at least' → ≥ (includes), 'less than' → <, 'at most' → ≤; infinite solutions as s > 75 includes 75.1, 76, ..., forever. For example, 'score more than 75' → s > 75, solutions: 76, 77, ... infinite integers or reals, graph: open ○ at 75 shaded right (○======>). The correct inequality is s > 75, matching choice C. Errors include using ≥ instead of >, including 75 wrongly, or reversing to <75, or saying finite solutions like only up to 100. Writing: (1) identify 'more than' as exclusive greater, (2) translate to >, (3) write s > 75; graphing would be open ○ at 75, shade right. Infinite solutions: uncountably many reals >75; context: scores above 75 qualify; mistakes: symbol mix-up (> vs ≥), not recognizing infinity.

This question tests writing inequalities like x > c or x < c from real-world constraints, understanding infinitely many solutions, and representing on number lines with proper boundary markers (●/○) and shading. Constraint words translate to symbols: 'at least' → ≥ (includes boundary: x ≥ 10 means 10 or more), 'at most' → ≤ (includes: x ≤ 50 means 50 or less), 'more than' → > (excludes boundary: x > 75 means above 75, not including 75), 'less than' → < (excludes: x < 60 below 60); inequalities have infinitely many solutions (x > 10 includes 11, 12, 13, ..., 1000, ...—continues forever, unlike equations with one solution); on a number line, mark boundary at c (for x > 10, mark 10), use closed ● if ≥ or ≤ (includes), open ○ if > or < (excludes), shade right for > / ≥ (greater values), left for < / ≤ (lesser values). For example, 'must have at least 10 tickets' → x ≥ 10 (x = tickets, 10 or more), solutions: 10, 11, 12, ... infinitely many (all non-negative integers ≥ 10), graph: ● at 10 shaded right (●======> ), includes 10 and all greater; or 'score more than 75' → x > 75 (above 75, excludes 75), graph: ○======> at 75 (open circle, shade right), solutions: 76, 77, 78, ... infinite. The correct solution is h = 48 (choice B), as h ≥ 48 includes 48 and taller. Errors are values below 48 like 47, 30, or 0 (choices A, C, D), not satisfying ≥ 48. To check: (1) identify 'at least' as ≥, (2) write h ≥ 48, (3) test values (48 works, 47 does not). Infinite solutions: all reals ≥ 48; mistakes treat it as > or pick non-solutions.

This question tests writing inequalities like b > c or b < c from real-world constraints, understanding that they have infinitely many solutions, and representing them on number lines with proper boundary markers (● for included, ○ for excluded) and shading. Constraint words translate to symbols: 'at least' means ≥ (includes), 'at most' means ≤ (includes boundary, like b ≤ 6 allows 6 or less), 'more than' means > (excludes), 'less than' means < (excludes); inequalities have infinite solutions unlike equations, and on a number line, use closed ● for ≥/≤, open ○ for >/<, shading right for greater and left for lesser. For example, 'at most 6' gives b ≤ 6 with solutions 0,1,2,...,6 infinitely many if reals, but here integers. The value not a solution is b=7, as it exceeds ≤6. A common error is thinking 6 is excluded like with <. Infinite solutions: all ≤6; context 'at most 6 books' allows 0 to 6. Mistakes: wrong symbol, confusing with more than.

This question tests writing inequalities like s > c or s < c from real-world constraints, understanding that they have infinitely many solutions, and representing them on number lines with proper boundary markers (● for included, ○ for excluded) and shading. Constraint words translate to symbols: 'at least' means ≥ (includes boundary), 'at most' means ≤ (includes), 'more than' means > (excludes, like s > 75 allows above 75 but not 75), 'less than' means < (excludes); inequalities have infinite solutions unlike equations, and on a number line, use closed ● for ≥/≤, open ○ for >/<, shading right for greater and left for lesser. For example, 'at least 13' gives a ≥ 13 with ● at 13 shaded right, infinite solutions like 13, 14, .... The correct number line is open circle at 75 shaded right, matching s > 75. A common error is using closed circle for >, including 75 wrongly, or shading left for less than. For graphing: (1) mark 75, (2) use open ○ since it excludes, (3) shade right for greater. Infinite solutions: all reals > 75; context like scores can be any real > 75, mistakes include circle type confusion.

This question tests understanding that inequalities like x > 10 have infinitely many solutions, contrasting with equations, and relating to real-world infinite possibilities. Constraint words aren't direct here, but recall 'more than' → > excludes boundary, and solutions are infinite (x > 10: 10.1,11,... forever). Example: x > 10 has infinite solutions like 11,12,... and all reals in between, graph: ○ at 10 shaded right. Correct statement is it has infinitely many solutions (all >10), matching choice D. Error: thinking it's like equation with one solution, or finite like 10 solutions, or none. For such inequalities: recognize infinite set; graphing reinforces with shading to infinity. Context: any number greater satisfies; mistakes: confusing with equations, not recognizing infinity.