Question

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

a) –10.5 < 3a
b) b6 ≤ 7
c) –4.5c > 9
d) –215 ≤ –52d
e) e – 13 ≥ 11

Answer 1

The inequalities from the given options that would have their symbols reversed when isolating the variable are 'c) –­4.5c > 9' and 'd) –­215 ≤ –­52d', because isolating the variable would involve dividing by negative numbers.

Step-by-step explanation:

In the context of inequality manipulation in Mathematics, when you are working to isolate the variable, the direction of the inequality symbol is reversed if you multiply or divide both sides of the inequality by a negative number. Let's apply this rule to determine which inequalities will have their symbols reversed when isolating the variable.

• a) –­10.5 < 3a
• b) b/6 ≤ 7
• c) –­4.5c > 9
• d) –­215 ≤ –­52d
• e) e –­ 13 ≥ 11

To find the answer, we'll look for inequalities involving multiplication or division by a negative number. When isolating the variable:

• c) Dividing by –­4.5 would reverse the symbol: –­4.5c > 9 becomes c < –­2.
• d) Dividing by –­52 would reverse the symbol: –­215 ≤ –­52d becomes d ≥ 215/52.

The inequalities where symbols would be reversed are therefore c and d.