Solve the inequality. Write the solution set in interval notation if possible. $$ (4 d+5)^{2}-6 $$ The solution set is $$ \square . \square $$

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Solve the inequality. Write the solution set in interval notation if possible. $$ (4 d+5)^{2}>-6 $$ The solution set is $$ \square . \square $$

UpStudy AI · Accepted Answer

1. Recognize that for any real number $$d$$, the expression $$(4d+5)^2$$ is a square, and thus it is always nonnegative:
   $$
   (4d+5)^2 \geq 0.
   $$

2. Since $$0 > -6$$, it follows that:
   $$
   (4d+5)^2 \geq 0 > -6.
   $$
   This means that the inequality $$(4d+5)^2 > -6$$ holds true for all real values of $$d$$.

3. Therefore, the solution set in interval notation is:
   $$
   (-\infty, \infty).
   $$
The solution set is all real numbers, written as $$ (-\infty, \infty) $$.

Solve the inequality. Write the solution set in interval notation if possible.

The solution set is

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Solve the inequality. Write the solution set in interval notation if possible. The solution set is