PSAT Math Question of the Day

1. $x<6$
2. $x\ge 5$
3. $x<6\ \text{or}\ x\ge 5$ (correct answer)
4. $x<6\ \text{and}\ x\ge 5$

Explanation: This is an OR compound inequality, meaning we solve each part separately and take the union of solutions. For $2x - 7 < 5$: add 7 to get $2x < 12$, then divide by 2 to get $x < 6$. For $3x + 1 ≥ 16$: subtract 1 to get $3x ≥ 15$, then divide by 3 to get $x ≥ 5$. Since this is OR, any value satisfying either inequality works, which means all real numbers (since every number is either less than 6 OR greater than or equal to 5). The key error is treating OR like AND; with OR, we take all values that satisfy at least one condition.