Question

Select all the inequalities that have symbols that will be reversed when the variable is isolated.

O 10.5 < 3a
O b ≥ 7
O 4.5c < 9
O 215 ≤ 52d
O e ≤ 13 ≥ 11

Answer 1

None of the provided inequalities will require inversion of the inequality symbol when isolating the variable, as they do not involve multiplication or division by negative numbers.

Step-by-step explanation:

In mathematics, especially when dealing with inequalities, the direction of an inequality symbol may need to be reversed under specific operations. This mainly occurs when both sides of an inequality are multiplied or divided by negative numbers. To determine which inequalities have symbols that will be reversed when isolating the variable, we must identify scenarios that involve these operations.

Let's examine the given inequalities one by one:

1. 10.5 < 3a: Isolating the variable 'a' does not require multiplying or dividing by a negative number, so the inequality symbol will remain unchanged.
2. b ≥ 7: Again, no multiplication or division by a negative number is required to isolate 'b', so the inequality symbol will remain unchanged.
3. 4.5c < 9: Isolating 'c' involves dividing by the positive number 4.5, which will not reverse the inequality symbol.
4. 215 ≤ 52d: Isolating 'd' necessitates division by the positive number 52, not reversing the inequality symbol.
5. e ≤ 13 ≥ 11: This expression involves a compound inequality; however, isolating 'e' would still not introduce any operation that would warrant reversing any inequality symbols.

In conclusion, none of the given inequalities will have their symbols reversed when isolating the variable as all apply operations with positive quantities. When working with inequalities, always remember to reverse the inequality symbol if you multiply or divide by a negative number.