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# Inequalities: Inequalities Involving an Absolute Value - the Variable Case

If \$\$|x| ≥ x+2\$\$, which of the following must be true?
Incorrect. [[snippet]] Try plugging in \$\$x = -5\$\$: >\$\$|{-5}| ≥ -5 + 2\$\$ >\$\$5 ≥ -3\$\$ While \$\$-5\$\$ works for the inequality in the question stem, it is not between \$\$-1\$\$ and \$\$1\$\$. Therefore, this answer choice is _not necessarily true_, and it should be eliminated.
Incorrect. [[snippet]] Try plugging in \$\$x = -5\$\$: >\$\$|{-5}| ≥ -5 + 2\$\$ >\$\$5 ≥ -3\$\$ Although \$\$-5\$\$ works for the inequality in the question stem, since \$\$-5 \le -4\$\$, you cannot yet eliminate this answer choice. Try plugging in \$\$x = -2\$\$: >\$\$|{-2}| ≥ -2 + 2\$\$ >\$\$2 ≥ 0\$\$ While \$\$-2\$\$ works for the inequality in the question stem, it is not \$\$\le -4\$\$. Therefore, this answer choice is _not necessarily true_, and it should be eliminated.
Correct. [[snippet]] Here's a possible elimination scenario: Try plugging in \$\$x = -5\$\$: >\$\$|{-5}| ≥ -5 + 2\$\$ >\$\$5 ≥ -3\$\$ Although \$\$-5\$\$ works for the inequality in the question stem, since \$\$-5 \le -1\$\$, you cannot yet eliminate this answer choice. However, \$\$x = -5\$\$ does eliminate answer choices A, B, and E. Try plugging in \$\$x = -2\$\$: >\$\$|{-2}| ≥ -2 + 2\$\$ >\$\$2 ≥ 0\$\$ Although \$\$-2\$\$ works for the inequality in the question stem, since \$\$-2 \le -1\$\$, you still cannot eliminate this answer choice. However, \$\$x = -2\$\$ eliminates answer choice D. By process of elimination, this answer choice (C) is the only one left standing. Therefore, it is correct.
Incorrect. [[snippet]] Try plugging in \$\$x = -5\$\$: >\$\$|{-5}| ≥ -5 + 2\$\$ >\$\$5 ≥ -3\$\$ While \$\$-5\$\$ works for the inequality in the question stem, it is not \$\$\ge 2\$\$. Therefore, this answer choice is _not necessarily true_, and it should be eliminated.
Incorrect. [[snippet]] Try plugging in \$\$x = -5\$\$: >\$\$|{-5}| ≥ -5 + 2\$\$ >\$\$5 ≥ -3\$\$ While \$\$-5\$\$ works for the inequality in the question stem, it is not greater than 1. Therefore, this answer choice is _not necessarily true_, and it should be eliminated.
\$\$x \ge 1\$\$
\$\$x \ge 2\$\$
\$\$x \le -1\$\$
\$\$x \le -4\$\$
\$\$-1 < x < 1\$\$