This question requires finding which given value of x satisfies the inequality 5 - 2x ≤ -9. Solve by subtracting 5 to get -2x ≤ -14, then divide by -2, reversing the inequality since dividing by negative, yielding x ≥ 7. Among the choices, only x=10 satisfies, as 5 - 2(10) = -15 ≤ -9 is true, while others like x=6 give -7 > -9. A key error is not reversing the inequality, which would incorrectly suggest x ≤ 7 and pick choice C. Another mistake is plugging in without solving, potentially missing the correct one. For verification questions, substitute each choice into the original inequality to confirm.

This question requires solving the inequality -3(2x - 5) ≥ 9 and identifying the correct solution set for x. Start by distributing the -3 to get -6x + 15 ≥ 9, then subtract 15 from both sides to obtain -6x ≥ -6. Now divide both sides by -6, and since you're dividing by a negative number, you must reverse the inequality symbol, resulting in x ≤ 1. A key error is forgetting to reverse the inequality when dividing by a negative, which might lead to x ≥ 1 as in choice B. Another common mistake is mishandling the distribution, potentially leading to incorrect bounds like in choices C or D. For inequalities involving negatives, always verify by testing a value in the solution set, such as x=0 which satisfies the original inequality.

The question requires modeling spending no more than $18 on 4 bags of chips at $2 each and $d$ drinks at $3 each. The inequality is $4 \times 2 + 3d \le 18$, or $8 + 3d \le 18$. This uses $\le$ for 'no more than.' A common error is using the wrong coefficients. Another pitfall is adding extras. Define costs clearly in budgeting problems.

This question asks for the inequality representing the age requirement of at least 16 for club membership. Let a be age, so a ≥ 16 models 'at least'. No solving needed. A common error is using > instead of ≥, excluding 16. Another mistake is reversing to ≤ or <. Include equality for 'at least' unless specified as more than.

The question asks to solve 10 - 4x ≤ 2x + 1. Add 4x to both sides to 10 ≤ 6x + 1, subtract 1 to 9 ≤ 6x, divide by 6 to 9/6 ≤ x, or x ≥ 3/2. Positive division keeps the direction. A common error is not flipping when needed, but here it's positive. Another is sign errors in adding terms. Test with x = 3/2.

This question requires an inequality for selling at least 80 items total, with 27 already sold and 6 per day for x days. Total items: 6x + 27, and 'at least' means ≥80. So, 6x + 27 ≥ 80. Choice B uses ≤, which is the opposite, and D rearranges terms incorrectly. A key error is using subtraction instead of addition for already sold items. Another pitfall is confusing 'at least' with 'at most.' For goal-oriented inequalities, ensure the symbol matches 'at least' (≥) and test with x=0 to check baseline.

This question requires solving the inequality -3(2x - 5) ≥ 9 and selecting the simplest solution set. First, distribute the -3: -6x + 15 ≥ 9. Subtract 15 from both sides: -6x ≥ -6. Divide by -6, and since dividing by a negative number, reverse the inequality: x ≤ 1. A key error is forgetting to reverse the inequality when dividing by -6, which would give x ≥ 1 incorrectly. Another pitfall is mishandling distribution, like treating -3(2x - 5) as positive. For inequalities involving negatives, always double-check the reversal step to avoid direction errors.

This question involves solving the compound inequality 2x - 7 < -1 AND x + 4 ≥ 6. Solve first: 2x < 6, so x < 3. Solve second: x ≥ 2. Intersection is 2 ≤ x < 3. Choice D represents 'or,' not 'and,' and A ignores the second condition. A common pitfall is solving one part and forgetting the intersection for 'and.' Another error is not handling the compound nature, leading to separate solutions. When dealing with 'and,' find overlapping values and test points in both originals.

This question requires a compound inequality for ages at least 16 and younger than 65. 'At least 16' means ≥16, and 'younger than 65' means <65. Combining gives 16 ≤ x < 65. Choice A uses >16, excluding 16, and C uses ≤65, including 65. A key error is mixing strict and non-strict symbols, like using ≤ for 'younger than.' Always translate words precisely: 'at least' is ≥, 'younger than' is <. For compound inequalities, ensure both parts are correctly joined with 'and.'

This question asks for the inequality modeling added boxes without exceeding 1,200 pounds, with 350 already loaded. Total weight is 55x + 350, and 'at most' means ≤1,200. So, 55x + 350 ≤ 1,200. Choice A uses ≥, opposite of capacity limit, and C subtracts 350 incorrectly. A common error is subtracting instead of adding the initial load. Another pitfall is using < instead of ≤, excluding the maximum. When modeling limits, verify by considering if equality is allowed, like exactly 1,200 pounds.