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Quiz 3
1. Convert the following sentence into symbols: "a number is greater than 17".
Solution: Let $x$ represent a number. Then "$x > 17$" accomplishes this.
2. Calculate
a.) $|-6|$
b.) $|2x-9|$ when $x=3$
Solution: For a.), $|-6|=6$.
For b.), substituting $x=3$ into the expression yields
$$|2 \cdot 3 - 9 | = |6-9| = |-3| = 3.$$
For c.), substituting $x=\dfrac{1}{2}$ into the expression yields
$$\left| 3 \cdot \dfrac{1}{2} + 4 \right| = \left| \dfrac{3}{2} + 4 \right| = \left| \dfrac{11}{2} \right| = \dfrac{11}{2}.$$
3. Combine like terms:
a.) $4x+3+2x^2-x+1-5x^2$
b.) $4@+3*-3@^2-2@+5*^2-*$
Solution: For a.)
$$4x+3+2x^2-x+1-5x^2=-3x^2+3x+4.$$
For b.)
$$4@+3*-3@^2-2@+5*^2-*=-3@^2+2@+5*^2+2*.$$
4. Calculate
a.) $\dfrac{1}{3} \div \left( - \dfrac{2}{3} \right)$
b.) $\dfrac{-\frac{2}{3}}{-\frac{5}{7}}$
Solution: For a.)
$$\dfrac{1}{3} \div \left( -\dfrac{2}{3} \right) = \dfrac{1}{3} \cdot \left( - \dfrac{3}{2} \right) = - \dfrac{3}{6} = -\dfrac{1}{2}.$$
For b.)
$$\dfrac{-\frac{2}{3}}{-\frac{5}{7}} = \left( -\dfrac{2}{3} \right) \left( -\dfrac{7}{5} \right) = \dfrac{14}{15}.$$
