Question

Solve each inequality −40<8+10(9+10n)

a) n>4
b) n<−4
c) n<4
d) n>−4

Answer 1

The inequality is solved by distributing the multiplication over addition, combining like terms, and isolating the variable n. The solution to the inequality −40 < 8 + 10(9 + 10n) is n > -1.38, which is most closely represented by option d) n > -4.

Step-by-step explanation:

To solve the inequality −40 < 8 + 10(9 + 10n), start by distributing the 10 into the parentheses:

-40 < 8 + 10 × 9 + 10 × 10n

-40 < 8 + 90 + 100n

Next, combine like terms:

-40 < 98 + 100n

Now, subtract 98 from both sides of the inequality:

-40 - 98 < 100n

-138 < 100n

Then, divide both sides by 100 to isolate n:

-1.38 < n

Finally, we can write the answer as:

n > -1.38

Looking at the given options, the closest one is:

n > -4