This question asks you to set up an inequality modeling the maximum spending on a rideshare with a $4 fee and $1.75 per mile, given at most $20 available. The total cost is 4 + 1.75m, and since you can spend up to $20, the inequality is 1.75m + 4 ≤ 20. Note that 'at most' includes equality, so use ≤ rather than <. A common error is using ≥, which would imply spending at least $20, but the situation requires no more than $20. Another pitfall is swapping the fee and per-mile rate, leading to incorrect expressions like choice C. When setting up inequalities from word problems, identify key phrases like 'at most' to determine the direction of the inequality symbol.

This question requires matching a number line with a closed circle at -1 and shading right to the inequality. Closed circle includes the point, so ≥ or ≤. Right shading means greater than or equal to -1, x ≥ -1. A key error is using > with closed circle. Another is left-shading confusion. Note circle type and direction for precise matching.

This question requires solving 7 - (1/2)x ≥ 1 for x. Subtract 7: -(1/2)x ≥ -6. Multiply by -2, reversing: x ≤ 12. Verify with x=12: 7 - 6 =1 ≥1, true. A common error is not reversing when multiplying by negative. Another mistake is arithmetic errors in isolation. Explicitly note reversal when multiplying by negatives.

This question asks for an inequality for flour f between 2 and 5 cups inclusive. 'Between inclusive' means 2 ≤ f ≤ 5. Use ≤ for both bounds since endpoints are included. A common error is using < > for exclusive, excluding 2 or 5. Another pitfall is mismatching bounds. Translate 'inclusive' to ≤ and ≥ for closed intervals.

This question requires solving 3x + 6 ≥ 0 or 2x - 5 < 1. First: x ≥ -2. Second: x < 3. The union covers all real x since intervals overlap completely. A common error is treating as 'and', giving -2 ≤ x < 3. Another mistake is incorrect solving of parts. For 'or' compounds, combine regions to see if they cover everything.

This question asks for an inequality for a phone bill of 30 + 0.10t ≤ 45. 'No more than' means ≤ for the upper limit. Subtract 30: 0.10t ≤ 15, but setup is key. A common error is using ≥, implying at least 45. Another pitfall is swapping fixed and variable costs. Read for limits like 'no more than' to set ≤ correctly.

This question requires solving 4(x - 3) ≤ 2x + 10 for x. Distribute: 4x - 12 ≤ 2x + 10. Subtract 2x: 2x - 12 ≤ 10. Add 12: 2x ≤ 22. Divide by 2: x ≤ 11. A common error is distributing incorrectly or forgetting to isolate x. When solving multi-step inequalities, perform operations step-by-step and check for reversal if negatives are involved.

This question asks for an inequality where a student spends x minutes on math plus 12 on vocabulary, totaling at least 45 minutes. The total time is x + 12 ≥ 45. Subtract 12: x ≥ 33, but the question seeks the setup. A common error is using ≤, implying an upper limit instead of minimum. Another pitfall is subtracting 12 from x. Identify 'at least' to use ≥ in minimum requirement problems.

This question requires matching a number line with an open circle at 6 and shading to the left to the correct inequality. Open circle means not included, so < or >. Left shading indicates less than 6, giving x < 6. A key error is interpreting as ≥6 due to misreading the shading direction. Another common mistake is using ≤ with the open circle. Pay attention to circle type and shading for accurate inequality matching.

This question asks which value satisfies 5 - 2x > 11. Subtract 5: -2x > 6. Divide by -2, reversing the symbol: x < -3. Test x = -4: 5 - 2(-4) = 13 > 11, true. A common error is not reversing when dividing by negative, leading to x > -3. Another mistake is testing values without solving first. For inequalities with negatives, explicitly note the reversal to ensure correct testing of options.