Evaluate variable expressions involving integers

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

Question source

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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