Question

Please answer this. thank you

Answer 1

Answer:  $(-\infty, -4]$

Curved parenthesis at negative infinity

Square bracket at -4

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Work Shown:

$5(x+4) \le 0 \\\\x+4 \le \frac{0}{5} \\\\x+4 \le 0 \\\\x \le 0-4 \\\\x \le -4$

The last inequality shown above is the same as saying $-\infty < x \le -4$

Converting this to interval notation leads to the final answer of $(-\infty , -4]$

Note the use of a square bracket at -4 to include this endpoint. We can never include either infinity, so we always use a parenthesis for either infinity.