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Inequalities: Overview

If $$4 < 7 - 2x < 12$$, how many integer solutions of $$x$$ are there?

Incorrect.

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Correct. [[Snippet]] Subtract $$7$$ from the inequality to isolate $$-2x$$. >$$4 - 7 < 7 - 2x - 7 < 12 - 7$$ >$$-3 < -2x < 5$$ Divide the inequality by $$2$$ to isolate $$-x$$. >$$\frac{-3}{2} < \frac{-2x}{2} < \frac{5}{2}$$ Multiply the inequality by $$-1$$ to isolate $$x$$. Do not forget to flip signs due to multiplication by $$-1$$. >$$-\left(\frac{-3}{2}\right) > -1(-x) > -\frac{5}{2}$$ >$$\frac{3}{2} > x > -\frac{5}{2}$$ Based on this, $$x$$ is more than $$-\frac{5}{2}$$ and less than $$\frac{3}{2}$$ (i.e., the integer values of $$x$$ are $$-2$$, $$-1$$, $$0$$, and $$1$$). Hence, there are four possible integer values for $$x$$.

Incorrect.

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Incorrect.

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Incorrect.

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