This is an absolute value question testing evaluation order. Choice B (−3) is correct — resolve each absolute value first: |−3| = 3, |−8| = 8, |2| = 2. Then apply the operations left to right: 3 − 8 + 2 = −3. Choice A (−13) ignores the absolute value symbols entirely, computing −3 − 8 + (−2) = −13 as if the bars weren't there. Choice C (3) likely comes from computing |−3 − (−8) + 2| = |7| = 7... or from incorrectly adding all values as positives: 3 + 8 + 2 = 13, then dividing or applying some other operation. Choice D (13) adds all three absolute values together — 3 + 8 + 2 = 13 — treating the minus sign between the first two as a plus sign. Pro tip: Absolute value bars are a grouping symbol — resolve them first to get the positive values, THEN carry out the arithmetic operations (subtraction, addition) between those values.

This is a fractional inequality requiring careful algebraic manipulation. Start with $ (x-1)/2 < 3 $, then multiply both sides by 2: $ x - 1 < 6 $. Add 1 to both sides: $ x < 7 $. In interval notation, this is $ (-\infty, 7) $, using a parenthesis since 7 is not included. Choice C incorrectly uses a bracket at 7, while choice B gives x < 5, likely from an arithmetic error. When multiplying inequalities by positive numbers, the inequality direction stays the same.

This is a linear inequality requiring basic algebraic manipulation. Starting with 5x - 3 ≤ 2, add 3 to both sides to get 5x ≤ 5. Divide by 5 (positive, so no sign flip) to get x ≤ 1. The solution is x ≤ 1, which matches choice A. This is a straightforward problem with no negative coefficients requiring sign flips. Choice B would represent the opposite inequality direction.

This linear inequality involves straightforward algebraic manipulation to isolate x. Start with x + 5 ≥ 8, then subtract 5 from both sides: x ≥ 3. The solution is x ≥ 3, meaning all values greater than or equal to 3 satisfy the inequality. This is a simple one-step inequality that requires only subtraction to solve. Choice B (x ≤ 3) represents the opposite inequality direction, which could result from misreading the inequality symbol or incorrectly flipping the direction. Since no multiplication or division by negative numbers occurs, the inequality direction remains unchanged.

This is an absolute value inequality of the form |expression| > constant, which represents values outside an interval. The inequality |x - 4| > 3 means the distance from x to 4 is greater than 3. Split into two cases: x - 4 > 3 or x - 4 < -3. Solve each: x > 7 or x < 1. The solution is x < 1 or x > 7, which matches choice D. Choice B would be the solution if we had |x - 4| < 3, representing values between 1 and 7.

This linear inequality involves isolating x through standard algebraic operations with positive coefficients. Start with 4x + 5 < 13, then subtract 5 from both sides: 4x < 8. Divide both sides by 4 (positive number, so no sign flip): x < 2. The solution is x < 2, meaning all values less than 2 satisfy the inequality. Choice C (x < 3) might result from arithmetic errors in the subtraction or division steps. Since we're working with positive coefficients throughout, the inequality direction remains unchanged at each step.

This is an absolute value question testing evaluation order. Choice B (−3) is correct — resolve each absolute value first: |−3| = 3, |−8| = 8, |2| = 2. Then apply the operations left to right: 3 − 8 + 2 = −3. Choice A (−13) ignores the absolute value symbols entirely, computing −3 − 8 + (−2) = −13 as if the bars weren't there. Choice C (3) likely comes from computing |−3 − (−8) + 2| = |7| = 7... or from incorrectly adding all values as positives: 3 + 8 + 2 = 13, then dividing or applying some other operation. Choice D (13) adds all three absolute values together — 3 + 8 + 2 = 13 — treating the minus sign between the first two as a plus sign. Pro tip: Absolute value bars are a grouping symbol — resolve them first to get the positive values, THEN carry out the arithmetic operations (subtraction, addition) between those values.

The interval notation (2,7] means all values greater than 2 but not including 2, up to and including 7. The parenthesis at 2 means x>2 (not x≥2), and the bracket at 7 means x≤7. Combined, this gives 2<x≤7. Choice A incorrectly includes 2 with ≥, choice C incorrectly excludes 7 with <, and choice D excludes both endpoints. When converting between interval and inequality notation, parentheses mean strict inequalities while brackets mean inclusive inequalities.

This is an inequality translation question testing mathematical language. Choice B (3n − 5 ≥ 10) is correct — "3 times a number n" → 3n. "5 less than" that quantity → subtract 5 → 3n − 5. "Is at least 10" → ≥ 10. Combined: 3n − 5 ≥ 10. Choice A (3n − 5 > 10) is close but uses strict inequality (>) instead of ≥. "At least" means "greater than OR equal to" — the ≥ symbol is required. Choice C (5 − 3n ≤ 10) reverses the subtraction — "5 less than 3n" means subtract 5 FROM 3n, which is 3n − 5, not 5 − 3n. These expressions are not equivalent. Choice D (3(n − 5) ≥ 10) misgroups the expression — it means "3 times the quantity (n minus 5)," which is different from "5 less than 3 times n." Pro tip: Build math phrases in the order they're stated. "5 less than 3n" means start with 3n, then subtract 5 — never flip the subtraction. And "at least" always translates to ≥, while "more than" translates to >.

This absolute value inequality represents distance and splits into two cases. |x - 3| < 4 means the distance from x to 3 is less than 4. This gives us -4 < x - 3 < 4. Adding 3 to all parts: -1 < x < 7. The solution is all values strictly between -1 and 7. Choice A shows the exterior solution (for ≥), while choices C and D have incorrect boundaries. For |expression| < constant, always get the interior solution between two bounds.