Definitions, Order of Operations, Simplifying Expressions, and Sets

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Example
1

Write each of the following in symbols:

The sum of \(x\) and \(5\) is less than \(2\).

The product of \(3\) and \(x\) is \(21\).

The quotient of \(y\) and \(6\) is \(4\).

Twice the difference of \(b\) and \(7\) is greater than \(5\).

The difference of twice \(b\) and \(7\) is greater than \(5\).

Example
9

Simplify the expression \(\dfrac{72-68}{5}\)

Example
10

Evaluate the expression \(\dfrac{23.6+16.3+18.9}{7-1}\)

Example
11

Evaluate \(a^2+8a+16\) when \(a\) is \(0, 1, 2, 3,\) and \(4\)

Example
12

Evaluate \(\dfrac{x-\overline{x}}{s}\) if \(x=186\), \(\overline{x}=135.8\), and \(s=35.2\).

Example
13

Evaluate \(\dfrac{s^2}{n}\) for the given values of the variables.

\(s=12\) and \(n=10\)

\(s=4.3\) and \(n=100\)

Example
14

If \(A=\{\text{all college students in the United States}\}\) and \(B=\{\text{all college students in Boston}\}\), then which of the following is true?

\(A\subset B\)

\(B\subset A\)

Example
15

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cup B\).

Example
16

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap B\).

Example
17

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap C\).

Example
18

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(B\cup C\).

Example
19

If \(A=\{1,2,3,4,5,6\}\), find \(C=\{x \mid x\in A \text{ and } x\geq4\}\).

**Mini Lecture**

Simplify.

\(4\cdot 2^2+5\cdot 2^3\)

\(40-10\div 5+1\)

\(3\left[2+4(5+2\cdot 3)\right]\)

Translate into symbols: The sum of \(x\) and \(y\) is less than the difference of \(x\) and \(y\).

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