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# Inequalities: Overview

Given that $$2x + 7 > 5$$ and $$5x - 13 < 7$$, all values of $$x$$ must be between which of the following pairs of integers?
Incorrect. [[snippet]] You might have gotten this answer if you made a sign error.
Correct. [[Snippet]] Isolate $$x$$ in both inequalities. For $$2x + 7 > 5$$, subtract $$7$$ to isolate $$2x$$. >$$2x + 7 - 7 > 5 - 7$$ >$$2x > -2$$ Divide by $$2$$ to isolate $$x$$. >$$\frac{2x}{2} > \frac{-2}{2}$$ >$$x > -1$$ For $$5x - 13 < 7$$, add $$13$$ to isolate $$5x$$. >$$5x - 13 + 13 < 7 + 13$$ >$$5x < 20$$ Divide by $$5$$ to isolate $$x$$. >$$\frac{5x}{5} < \frac{20}{5}$$ >$$x < 4$$ Based on this, $$x$$ must be greater than $$-1$$ and less than $$4$$. >$$-1 < x < 4$$ Hence, this is the correct answer.
Incorrect. [[snippet]] Carefully check your work.
Incorrect. [[snippet]] Carefully check your work. You may have gotten this answer if you made sign errors when solving each inequality.
$$-4$$ and $$-1$$
$$-1$$ and $$4$$
$$-4$$ and $$1$$
$$-2$$ and $$5$$
$$2$$ and $$5$$