## Algebra 2 Tutorial

*Evaluate variable expressions involving integers*

#### Intro

Starting with the basics is variables (symbols for an unknown number, usually a letter like x or y) involving integers (an integer is a whole number, not a fraction). “Evaluate variable expressions involving integers” is the same as saying “solve for x using whole numbers”.

With this, we need to know the following:

1) We can use parentheses (or an asterisk) to substitute as a multiplication symbol:

Parentheses: 1(2)=2

Asterisk: 1 * 2 = 2

Basic multiplication symbol (which won’t be used but shown for demonstration purposes only): 1 × 2 = 2

2) A negative times a negative is a positive -1 * -1 = 1 OR (-1)(-1)=1

3) Adding a negative is the same as subtracting:

3 + (-3) = 0 is the same as 3 + -3 = 0 which is the same as 3 – 3 = 0 (basic subtracting)

#### Sample Problem

Evaluate the expression for b = 2.

8b – 15 =

Evaluate means to solve the problem by “filling in” the number for the letter.

#### Solution

In this scenario, we need to realize the “plug and chug” idea. Plug in the number 2 for the letter b and chug (like moving forward with a train).

8b-15 is the same as multiplying 8 by b, which we know is 2 from the problem that states b=2 (then we subtract 15). We can use parentheses to substitute as a multiplication symbol:

8(2)-15 is the same as 8 * 2 – 15

Since 8*2=16, we can fill in the rest of it as:

16-15=1

The answer is: 1

Quickly:

Problem:

Evaluate the expression for b = 2.

8b – 15 =

Solution:

8(2)-15=

16-15=1

————————————————

Another:

Evaluate the expression for p = -1.

-18p – 16 =

-18(-1)-16=

18-16=2

[A negative times a negative is a positive]

Another problem:

Evaluate the expression for u = -14.

1 + u =

1+(-14)=-13

Another problem:

Evaluate the expression for t = 18.

t – 15 =

(18)-15=3

Another problem:

Evaluate the expression for m=-1

7 + 13m =

7 + 13(-1)=

7 + -13 is the same as 7 – 13

7 – 13 = 6

Another problem:

Evaluate the expression for g = -9 and h = -1.

-6gh + h =

-6(-9)(-1)=

(Since we start with a negative, the next two negatives cancel each other out, so we’re left with a negative number. We need to multiply to get our answer)

This is the same as -6*-9*-1 (The asterisk is a stand-in for “x” because “x” is used often in Algebra and can get quite confusing, so we substitute).-9*-1=9

-6*9=-54

OR

From the beginning:

-6 * -9 * -1 =

-6 * -9 = 54 * -1 = -54

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