The correct answer is A. The inequality $$y ≤ 3.5$$ means $$y$$ can be any value less than or equal to $$3.5$$. Jamie's value $$3\frac{1}{4} = 3.25$$ satisfies this since $$3.25 ≤ 3.5$$. Alex's value $$3.6$$ does not satisfy this since $$3.6 > 3.5$$. Choice B incorrectly suggests rounding changes inequality relationships. Choice C incorrectly suggests 'closeness' rather than the actual inequality relationship. Choice D incorrectly restricts solutions to integers only.

The correct answer is B. Safe operation requires $$t ≥ -5$$ AND no malfunction requires $$t ≤ 8$$ (the opposite of $$t > 8$$). Both conditions must be satisfied simultaneously, giving us $$-5 ≤ t ≤ 8$$. Choice A incorrectly uses OR instead of AND and wrong inequality directions. Choice C incorrectly excludes the boundary values $$-5$$ and $$8$$. Choice D describes conditions where at least one problem occurs (either too cold or malfunction), not safe operation.

The correct answer is B. To satisfy both inequalities simultaneously, we need the intersection: $$m ≥ -1$$ AND $$n < 3$$. This means $$-1 ≤ P < 3$$, which includes $$-1$$ (due to the ≥ symbol) but excludes $$3$$ (due to the < symbol). Choice A incorrectly includes $$3$$. Choice C incorrectly assumes only one value works. Choice D describes values that satisfy neither inequality or only one of them.

The correct answer is B. In the compound inequality $$-4 < w ≤ -1$$, the symbol $$<$$ at $$-4$$ means $$w$$ is strictly greater than $$-4$$ (not equal), so $$-4$$ gets an open circle. The symbol $$≤$$ at $$-1$$ means $$w$$ is less than or equal to $$-1$$ (including equal), so $$-1$$ gets a closed circle. Choice A incorrectly excludes $$-1$$. Choice C reverses the circle types. Choice D incorrectly includes $$-4$$.

This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2°C is warmer than -5°C), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For points at -7 and -3 on the number line, -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 is positioned to the right of -7, meaning -7 < -3 or equivalently -3 > -7. The correct inequality is -7 < -3 because -7 is to the left of -3 on the number line, which is choice B. A common error is magnitude comparison for negatives, like -7 > -3 because 7 > 3 (but actually -7 < -3), or claiming numbers increase leftward (reversing direction), or equality because both negative. When interpreting, the inequality symbol shows position (< means left of, > means right of), and for negatives, the less negative is greater and farther right, like |-7| > |-3| but -7 < -3 since -7 is left; comparing same-sign, magnitudes reverse for negatives. The number line helps visualize (left < right), aiding in plotting and seeing the right one is greater, avoiding mistakes like reversing position or magnitude errors.

This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2 is higher than -5 m below sea level), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For points P at -1 and Q at 4 on the number line, -1 is to the left (negative, smaller), 4 is to the right (positive, larger), so -1 is left of 4, meaning -1 < 4. The correct inequality is -1 < 4 because -1 is to the left of 4 on the number line, which is choice C. A common error is thinking farther from zero means less (but for different signs, positive is greater), or claiming -1 > 4 because left (reversing meaning), or equality due to different sides. When interpreting, the inequality symbol shows position (< means left of, > means right of), and for different signs, positive always > negative like 4 > -1 since right; comparing signed, plot to see right is greater. The number line visualizes order (left < right), helping avoid mistakes like position reversal or zero confusion.

This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. In number line interpretation, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left being less than right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For points x and y both at -8 on a number line, they are at the same position, so x = y, meaning inequalities like x <= y or x >= y are true since they include equality. The correct statement is x <= y because both points are at the same position on the number line, which matches choice B. A common error is claiming x > y despite same (choice A), or x < y with left greater (choice C), or x >= y false because negative (choice D), ignoring equality for negatives. When interpreting equals, <= or >= apply; comparing same negatives shows equality like positives. The number line helps by showing identical spots, with mistakes like assuming negatives can't equal or direction issues.

This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct interpretation is that on a number line, -2 is to the right of -5, so -2 is greater, matching choice A. A common error is reversing positions, like claiming -2 is left of -5 so greater (choice B), or using magnitude comparison for negatives like 5 > 2 so -5 > -2 (choice C), or thinking negatives cannot be compared (choice D). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct inequality is a < b because -1 is to the left of 4, matching choice B. A common error is reversing the inequality like a > b because left or negatives greater (choices A and D), or thinking opposite sides mean equal (choice C). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct interpretation is 2 > -3 because 2 is to the right of -3 on the number line, matching choice B. A common error is claiming negatives are always greater than positives (choice A or D), or that being farther from 0 makes -3 greater (choice C), or they are equal due to opposite sides (choice D). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.