Absolute Value Inequalities Quiz 1

Question 1

If $$\left| 6t+15 \right| < 0$$ , which of the following express the allowable range for $$t$$ ?

Accepted Answer

No solution

Answer

$$\left( -\infty ,-\dfrac{5}{2} ight]	ext{ or }\left[ \dfrac{5}{2},\infty  ight)$$

Answer

$$\left[ -\dfrac{5}{2},\dfrac{5}{2} \right]$$

Answer

$$\left( -\dfrac{5}{2},\dfrac{5}{2} \right)$$

Question 2

If $$\left| 25-13q \right|\le 2$$ , which of the following express the allowable range for $$q$$?

Accepted Answer

$$\left[ \dfrac{23}{13},\dfrac{27}{13} \right]$$

Answer

$$\left[ -\dfrac{23}{13},\dfrac{27}{13} \right]$$

Answer

$$\left[ -\dfrac{27}{13},\dfrac{23}{13} \right]$$

Answer

$$\left[ -\dfrac{23}{13},-\dfrac{27}{13} \right]$$

Question 3

If $$\left| 8y+12 \right|\ge 5$$, which of the following expresses the allowable range for $$y$$ ?

Accepted Answer

$$\left( -\infty ,-\dfrac{17}{8} ight]	ext{ or }\left[ -\dfrac{7}{8},\infty  ight)$$

Answer

$$\left( -\infty ,-\dfrac{17}{8} ight)	ext{ or }\left( -\dfrac{7}{8},\infty  ight)$$

Answer

$$\left[ -\dfrac{17}{8},-\dfrac{7}{8} \right]$$

Answer

$$\left( -\infty ,-\dfrac{15}{8} ight]	ext{ or }\left( -\dfrac{7}{8},\infty  ight]$$

Question 4

Find the absolute value inequality statement that corresponds to the inequalities $$x\le 23$$ or $$x\ge 30$$?

Accepted Answer

$$\left| x-26.5 \right|\ge 3.5$$

Answer

$$\left| x+22.5 \right|\ge 3.5$$

Answer

$$\left| x-26.5 \right|\le 3.5$$

Answer

$$\left| x+22.5 \right|\le 3.5$$

Question 5

If $${{(x-2)}^{2}}-3x+10 < \left| 2x-8 \right|$$ , which of the following expresses the allowable range for $$x$$ ?

Accepted Answer

$$2 < x < 3$$

Answer

$$2 < x < 5$$

Answer

$$5 < x < 7$$

Answer

$$-3 < x < -2$$