Inequalities: Overview
Given that $$1 + 3x > 4$$ and $$2x - 3 < 5$$, all values of $$x$$ must be between which of the following pairs of integers?
Correct.
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Isolate $$x$$ in both inequalities. For $$1 + 3x > 4$$, subtract $$1$$ to isolate $$3x$$.
>$$1 + 3x - 1 > 4 - 1$$
>$$3x > 3$$
Divide by $$3$$ to isolate $$x$$.
>$$\frac{3x}{3} > \frac{3}{3}$$
>$$x > 1$$
For $$2x - 3 < 5$$, add $$3$$ to isolate $$2x$$.
>$$2x - 3 + 3 < 5 + 3$$
>$$2x < 8$$
Divide by $$2$$ to isolate $$x$$.
>$$\frac{2x}{2} < \frac{8}{2}$$
>$$x < 4$$
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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Make sure you solve the two inequalities for $$x$$ (without a coefficient).
Incorrect.
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Carefully check your work.
Incorrect.
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Make sure you isolate the variable before dividing by the coefficient.
Incorrect.
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Carefully check your work.
$$3$$ and $$8$$
$$1$$ and $$4$$
$$3$$ and $$12$$
$$\frac{4}{3}$$ and $$\frac{5}{2}$$
$$-5$$ and $$1$$
