Question

C = 12 is a solution for 4c - 2 > 46

Answer 1

Answer: False, it's not a solution

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Explanation:

Replace every copy of c with 12. Then simplify.

4c - 2 > 46

4*12 - 2 > 46

48 - 2 > 46

46 > 46 ... false

The statement is false because there isn't a number that's larger than itself (or smaller than itself).

Since the last statement is false, this means the first inequality is false when c = 12.

Therefore, c = 12 is not a solution.

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Another approach:

Let's isolate c in the original inequality.

4c - 2 > 46

4c > 46+2

4c > 48

c > 48/4

c > 12

The solution set consists of numbers larger than 12. We leave 12 itself out of the solution set.

This is because c > 12 would be 12 > 12 which is false.