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The absolute value symbol is a shifted backslash key.
4 - 3*|m + 2| > -14
We start by isolating the absolute value expression. Subtract 4 from both sides of the inequality, and then divide both sides by -3. (NOTE: remember that whenever an inequality is multiplied by or divided by a negative amount, we must reverse the direction of the inequality symbol.)
4 - 4 - 3*|m + 2| > -14 - 4
-3*|m + 2| > -18
|m + 2| < -18/(-3)
|m + 2| < 6
Next, we use the definition of absolute value expressions to remove the absolute value symbols. The definition tells us that m + 2 is less than 6 units away from zero. But, this means less than 6 units away from zero on either side! So, we get:
-6 < m + 2 < 6
To solve for m, we subtract 2 from each expression.
-6 - 2 < m + 2 - 2 < 6 - 2
-8 < m < 4
If you check these two numbers by substituting them for m in the original inequality, you will find that they result in -14 > -14.
This tells us that these two numbers are the borderline values that separate the values of m that satisfy the inequality from the values that do not.
Try choosing values for m that are between -8 and 4. The original inequality will always evaluate to a true statement. Choosing values smaller than -8 or larger than 4 will not work.
~ Mark
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