Question

What is the reason for each step in the solution of the inequality?4(x+6)>−5(x+5)−14Select the reason for each step from the drop-down menus. 4(x+6)>−5(x+5)−14 Given 4x+24>−5x−25−14Choose... 4x+24>−5x−39Choose... 4x+63>−5xAddition Property of Order63>−9xSubtraction Property of Order −7

Answer 1

In the second step, they used the Distributive Property of Multiplication over a sum:

a(b + c) = ab + ac

4(x + 6) = 4x + 4*6 = 4x + 24

and

5(x + 5) = 5x + 5*5 = 5x + 25

In the third step, they added the numbers -25 and -14, which resulted in -39.

In the last step, they found an equivalent inequality by dividing both sides by the same factor (-9):

63/(-9) = -63/9 = -7

-9/(-9) = 9/9 = 1

Notice that the symbol < eas changed to >. This happens when we multiply an inequality by a negative number.