$Unknown environment 'tabular'$ answer.
a. $(- \infty, - \frac{57}{16}]$
b. $[- \frac{57}{16}, \infty)$
c. $(- \infty, - \frac{5}{8}]$
d. $[- \frac{5}{8}, \infty)$

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Final Answer: $a . (- \infty, - \frac{57}{16}]$ and $d . [- \frac{5}{8}, \infty)$

Steps

Step 1 ：Simplify the expression: $12 x^{2} + (13 + 14 + 15 + 16) x - (18 + 19 + 20)$

Step 2 ：Calculate the solutions: $x = - \frac{29}{12} + \frac{5 \sqrt{61}}{12}$ and $x = - \frac{5 \sqrt{61}}{12} - \frac{29}{12}$

Step 3 ：Determine the intervals: $x = - \frac{29}{12} + \frac{5 \sqrt{61}}{12}$ belongs to option d, and $x = - \frac{5 \sqrt{61}}{12} - \frac{29}{12}$ belongs to option a

Step 4 ：Final Answer: $a . (- \infty, - \frac{57}{16}]$ and $d . [- \frac{5}{8}, \infty)$

Unknown environment 'tabular'Unknown environment 'tabular' answer.a. (−∞,−5716]b. [−5716,∞)c. (−∞,−58]d. [−58,∞)

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$Unknown environment 'tabular'$ answer.
a. $(- \infty, - \frac{57}{16}]$
b. $[- \frac{57}{16}, \infty)$
c. $(- \infty, - \frac{5}{8}]$
d. $[- \frac{5}{8}, \infty)$