This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context, here verifying a value. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left. To verify x=-2 in 3x-5<4, substitute: 3(-2)-5=-6-5=-11, and -11<4 is true, so yes it satisfies. The correct choice A shows this calculation and confirmation. Errors include wrong computation like to 1<4 still yes but incorrect (choice B), claiming -11>4 (choice C), or to 11<4 false (choice D). Steps are substituting the value, simplifying left side, comparing to right with <, and concluding based on truth. Mistakes involve arithmetic errors like sign mishandling or adding instead of subtracting, or reversing the inequality check.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context with whole numbers. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this quiz problem needing more than 75 points from 68 plus 2 per quiz, set up 68+2q>75, solve by subtracting 68 (2q>7), dividing by 2 (q>3.5 since 2>0, no flip), and interpret smallest whole number as 4 quizzes since q must be integer. The correct choice A shows q>3.5 and at least 4 quizzes. Errors include using ≥ instead of > (choice C with q≥3.5), rounding down incorrectly (choice B with at least 3), or misstating as exactly 4 (choice D). Steps include: (1) translate 'more than 75' to >75, (2) solve with inverse operations, (3) for strict >, use open circle if graphing, (4) interpret with ceiling to next integer for 'at least'. Context requires whole quizzes, and mistakes involve boundary type or forgetting to round up for strict inequality.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this phone plan starting at $50 credit minus $2.50 per data day, at least $20 remaining, set up 50-2.5d≥20, solve by subtracting 50 (-2.5d≥-30), dividing by -2.5 (d≤12, flip since negative), and interpret as 12 or fewer days. The correct choice A shows d≤12 and interpretation of 12 days or fewer. Errors include no flip (choice B with d≥12), wrong constants (choices C and D with d≤30 or d≥30). Steps include: (1) translate 'at least $20' to ≥20, (2) solve by subtracting and dividing with flip for negative, (3) graph would be closed dot at 12 shaded left, (4) interpret as d≤12. Mistakes often involve forgetting to flip when dividing by negative or direction errors.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context with whole numbers. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this quiz problem needing more than 75 points from 68 plus 2 per quiz, set up 68+2q>75, solve by subtracting 68 (2q>7), dividing by 2 (q>3.5 since 2>0, no flip), and interpret smallest whole number as 4 quizzes since q must be integer. The correct choice A shows q>3.5 and at least 4 quizzes. Errors include using ≥ instead of > (choice C with q≥3.5), rounding down incorrectly (choice B with at least 3), or misstating as exactly 4 (choice D). Steps include: (1) translate 'more than 75' to >75, (2) solve with inverse operations, (3) for strict >, use open circle if graphing, (4) interpret with ceiling to next integer for 'at least'. Context requires whole quizzes, and mistakes involve boundary type or forgetting to round up for strict inequality.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this phone plan starting at $50 credit minus $2.50 per data day, at least $20 remaining, set up 50-2.5d≥20, solve by subtracting 50 (-2.5d≥-30), dividing by -2.5 (d≤12, flip since negative), and interpret as 12 or fewer days. The correct choice A shows d≤12 and interpretation of 12 days or fewer. Errors include no flip (choice B with d≥12), wrong constants (choices C and D with d≤30 or d≥30). Steps include: (1) translate 'at least $20' to ≥20, (2) solve by subtracting and dividing with flip for negative, (3) graph would be closed dot at 12 shaded left, (4) interpret as d≤12. Mistakes often involve forgetting to flip when dividing by negative or direction errors.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context. Solving is similar to equations but preserves inequality direction—for $px + q \le r$: subtract q ($px \le r - q$), divide by p ($x \le(r - q)/p$ if p>0, flip to $x \ge \ldots$ if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: $5v + 10 \le 100$ → $5v \le 90$ → $v \le 18$ graphs as closed dot at 18, shaded left. In this gym context with $10 plus $5 per visit and at most $100, $v \le 18$ means you can visit 18 or fewer times to stay within budget, including 18 exactly. The correct choice B interprets this accurately. Errors include thinking exactly 18 (choice A), reversing to 18 or more (choice C), or excluding 18 (choice D). Steps include solving to $v \le 18$ as in the example, then interpreting in context (18 or less visits, realistic non-negative integers 0 to 18). Mistakes often are misinterpreting ≤ as > or excluding the boundary, ignoring context like positive visits.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context, especially with whole numbers. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left. For needing more than 75 points with 68 current and +2 per quiz, set up 68+2q>75, solve by subtracting 68 (2q>7), dividing by 2 (q>3.5), and since quizzes are whole, q≥4 as q=4 gives 76>75 but q=3 gives 74≤75. The correct choice A reflects this with q>3.5 so q≥4 whole quizzes. Errors include using ≥75 leading to q≥3 incorrectly (choice B), dividing wrong to q>7 (choice C), or ignoring whole numbers by suggesting q=3.5 (choice D). Steps are translating 'more than' to >75, solving with inverse operations keeping direction, interpreting for whole q≥4 since context requires integers (can't do half quizzes, round up). Mistakes involve direction errors like using ≥ instead of >, forgetting to round up for strict inequality, or calculation slips like dividing 7 by 2 incorrectly.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this free time problem with x minutes, minus 15 for homework, at least 25 left, the correct inequality is x-15≥25, solving to x≥40, graphed closed dot at 40 shaded right. The correct choice A shows x-15≥25, x≥40, closed dot at 40 shaded right. Errors include wrong direction (choice B with ≤40 shaded left), reversed subtraction (choice C with 15-x≥25 to x≤-10), or addition (choice D with x+15≥25 to x≥10). Steps include: (1) translate 'at least 25 left' to remaining ≥25, so x-15≥25, (2) solve adding 15, no flip, (3) graph closed right for ≥, (4) interpret as x≥40. Common mistakes are inequality setup direction or confusing subtraction with addition.

This question tests solving two-step linear inequalities from word problems, graphing solution sets on number lines (open/closed dots, directional shading), and interpreting in context. Solving is similar to equations but preserves inequality direction—for px+q≤r: subtract q (px≤r-q), divide by p (x≤(r-q)/p if p>0, flip to x≥... if p<0); graphing uses closed dot ● for ≤ or ≥ (includes boundary), open ○ for < or > (excludes), shade left for < or ≤ (toward smaller), right for > or ≥ (toward larger); example: 5v+10≤100 → 5v≤90 → v≤18 graphs as closed dot at 18, shaded left for 18 or less. For this free time problem with x minutes, minus 15 for homework, at least 25 left, the correct inequality is x-15≥25, solving to x≥40, graphed closed dot at 40 shaded right. The correct choice A shows x-15≥25, x≥40, closed dot at 40 shaded right. Errors include wrong direction (choice B with ≤40 shaded left), reversed subtraction (choice C with 15-x≥25 to x≤-10), or addition (choice D with x+15≥25 to x≥10). Steps include: (1) translate 'at least 25 left' to remaining ≥25, so x-15≥25, (2) solve adding 15, no flip, (3) graph closed right for ≥, (4) interpret as x≥40. Common mistakes are inequality setup direction or confusing subtraction with addition.