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Patterns and Algebra
L1: Evaluating Algebraic Expressions
and Equations
L2: Solving Algebraic Expressions
Equations and Expressions

Equation


An equation has an
equal sign making the
expression equal to a
specific number.
Example
2a +3b
a= 5
b= 9

Expression

Determine a numerical
value for that expression

Always follow the order
of operations

Example
X + 7 = 15
Example 1
2a + 3b
a= 5
b= 9

Substitute the values for a and b
2 (5) + 3 (9)
10 + 27=
37
Example 2
Evaluate the expression
2x² - 4x + 9 when x =6

Plug in 6 wherever you see x.
2(6)² - 4x + 9
72 - 24 + 9=
57
Example 3
Pens cost $.50 and pencils cost $.30. Given the
equation C= $.50 + $.30y where C= cost, x=
pens, and y= pencils, calculate the cost of
buying 7 pens and 9 pencils
C= $.50 + $.30y
C=$.50 (7) + $.30 (9)
C= $3.50 + $2.70
C=$6.20
Extended Constructed Response

On a recent math quiz, the seventh grade students in Mrs.
Lopez class were asked to evaluate the expression 4r + 3s – 2t
when r = 6, s = 4, and t = 3. Paulina evaluated the expression
and determined its value to be 57.

Is she correct or incorrect?


If Paulina’s response is correct show the work proving her
answer is correct.
However, if you believe that Paulina’s response is incorrect,
determine what she did incorrectly and show the correct way
to evaluate the expression.
Solving Algebraic Equations
Four Steps for Solving Equations
1.
Isolate

2.
Inverse

3.
Use the inverse operation to get the variable by
itself
Solve

4.
Identify the variable by putting a box around it
Do the math! You may have to work backwards
in order to get an answer.
Check

Plug your answer into the original equation.
Example 1
X + 19 = 45
X + 19 = 45
- 19 -19
X = 26
26 + 19 = 45
45= 45
Example 2
9X =144
9X =144
9X =144
9
9
X= 16
9(16) = 144
144=144
Example 3
3x – 21 = 63
3x – 21 = 63
+ 21 +21
3X= 84
3 3
X= 28
3 (28) – 21 = 63
84-21= 63
63=63