Solve each polynomial inequality in Exercises 1–42 and graph the ...

Question

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2+16x<−5

Accepted Answer

Saw the following polynomial inequality where you have five X squared plus eight X is less than negative three. I'm going to write this in standard form by moving my negative three to the other side. So we add three to both sides. You can get five X squared plus eight X plus three. It's less than zero. Now, we want to factor this polynomial five X squared plus eight X plus three gives any method, but this should factor to five X plus three times X plus one. It's less than zero. Now, I'm going to figure out what our interval is. I'm gonna set five X plus three less than zero and X plus one less than zero. Whichever one is our negative answer. We will change our side our symbol. But first, let's take a look, we have this mainstream five X less than negative 35 X, less than negative three fits Over here. subtract one X Less than Native one. Now, both of these are negative. So you want to see which one is smaller in this case, X less than negative one is smaller. I'm gonna change that sign then two X greater than negative one, we can then write our interval as negative one to negative 3/5. This makes sense is for our problem answer. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2+16x<−5

Key Concepts

Polynomial Inequalities

Graphing on a Number Line

Interval Notation

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