Question

1. (l121) is the following sentence true? the rules for undoing multiplication and division are exactly the same for inequalities as they are for equations. a) yes b) no c) maybe d) sometimes e) not applicable 2. (l127) is the following sentence true? in a compound inequality, the word “or” means that a solution must solve either of the individual inequalities, but not both. a) yes b) no c) maybe d) sometimes e) not applicable 3. (l126) simplify the irrational expression: \\(\sqrt{45}\\) a) \\(\sqrt{5}\\) b) \\(3\sqrt{5}\\) c) \\(5\sqrt{3}\\) d) \\(\sqrt{15}\\) e) 9

Explanation:

Step1: Analyze multiplication/division rules for inequalities and equations

For equations, when we multiply or divide both sides by a non - zero number, the equality holds. For inequalities, when we multiply or divide both sides by a positive number, the inequality sign remains the same. But when we multiply or divide both sides by a negative number, the inequality sign flips. So the rules are not exactly the same.

Step2: Analyze "or" in compound inequalities

In a compound inequality with "or", a solution can solve either of the individual inequalities or both. For example, in \(x < 2\) or \(x>0\), \(x = 1\) satisfies both parts and is a solution.

Step3: Simplify the square - root expression

We know that \(45=9\times5\). So \(\sqrt{45}=\sqrt{9\times5}\). According to the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 9\), \(b = 5\) and \(a\geq0\), \(b\geq0\)), we have \(\sqrt{45}=\sqrt{9}\cdot\sqrt{5}=3\sqrt{5}\).

Answer:

1. b) No
2. b) No
3. b) \(3\sqrt{5}\)