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6 votes
6 votes
Solve the inequality.
|x − 14| + 7 > 4

User Oluwatoyin
by
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1 Answer

19 votes
19 votes

Answer: Infinitely many solutions (ie set of all real numbers)

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Step-by-step explanation:

First we subtract 7 from both sides

|x - 14| + 7 > 4

|x - 14| + 7-7 > 4-7

|x - 14| > -3

Recall that absolute value is never negative. So the |x-14| will never dip below zero.

In other words, the smallest |x-14| can possibly get is 0.

Because 0 > -3 is always true, this means |x − 14| > -3 is always true for any x value you pick.

Therefore, there are infinitely many solutions. The x value can be any real number.

User Ranieribt
by
3.1k points