Solve each inequality. Give the solution set using interval notat...

Question

Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9.3(x + 5) + 1 ≥ 5 + 3x

Accepted Answer

Welcome back everyone. In this problem, we want to use the square root property to solve the quadratic equation. Eight squared minus 216 equals zero. For our answer choices A is H equals negative six multiplied by the spirit of two and six multiplied by the spirit of two, B is H equals negative three, multiplied by the spirit of six and three multiplied by the spirit of six C is H equals negative two multiplied by the spirit of six and two multiplied by the spirit of six and D is H equals negative six multiplied by the square root of six and six multiplied by the square root of six. Now, what do we know? Well, we want to solve our quadratic equation and to do that, we want to use the square root property. Now recall that the square root property says that if I have the square root of a product A B is the same thing as the square of A multiplied by the square of B. In other words, the spirit of the product equals the square root of each term multiplied by each other. So we can use that to help us to solve for our problem. No, let's do that. So if we can find some square root that will apply in our term in our, in our, in our equation, then we'll be able to apply and solve. So we're working with eight squared minus 216 equals zero. That means if we add 216 to both sides, then eight squared equals 216. Now, if a squared is 216 that means H equals the square root of 216 but 216 isn't a square number. So that's where our square root property comes in. Because if we can think of some square number, that's a part of the product for 216 then we can simplify to get that integer and not written as a square root. So let's think about it. 216. What square number can come from that? How about 30 36? Remember that 216 equals six multiplied by 36. So we can use that to help us because we can rewrite H as the square root of six multiplied by 36. And no using the square root property that could be written as the square root of 36 multiplied by the square root of six, the square root of 36 equals six plus or minus six. And we'd still have to write route six as our exact answer. So that tells us that H either equals six multiplied by the root of six, or it equals negative six multiplied by the spirit of six. And when we look back on our answer choices, that would have been answer choice. D thanks a lot for watching everyone. I hope this video helped.

Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9.3(x + 5) + 1 ≥ 5 + 3x

Key Concepts

Inequalities

Interval Notation

Algebraic Manipulation

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