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.
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You might have gotten this answer if you made a sign error.
Correct.
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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.
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Carefully check your work.
Incorrect.
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Carefully check your work. You may have gotten this answer if you made sign errors when solving each inequality.
Incorrect.
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Check your calculations.
$$-4$$ and $$-1$$
$$-1$$ and $$4$$
$$-4$$ and $$1$$
$$-2$$ and $$5$$
$$2$$ and $$5$$
