1. Objective
translate verbal sentences into equations

2. Section 2.4, “Variables and Equations”
mathematical sentence formed by placing an “=“ between two expressions
y – 8 = 12
22 = 14 + z
x ÷ 5 = 30
11a = 121

3. Equation x
+ 7 = 10
Left side
Right side
‘x’ has to be 3 in order to make the equation balanced.
Like a scale, the left side and right side must be the same in order to be balanced!

4. Writing Algebraic Expressions
Operation
Verbal Phrase
Expression
Addition
Sum, plus, total, more than, increased by
5 + n k + 12
Subtraction
Difference, less than, minus, decreased by
12 – p x – 12
Multiplication
Product, times, of, multiplied by
3 x (d)
(n)(w) p ∙ k
Division
Quotient, divided by, divided into
k/ ÷ r
Writing Equations
Symbol
Meaning
Key phrases =
Is equal to
The same as, is

5. Translate verbal phrases into equations
the difference of a number k and 8 is 12.
k – 8 = 12
6n = 24 b.
the product of 6 and a number n is 24.
y + 5 = 13 c.
the sum of a number y and 5 is 13.
z ÷ 2 = 7 d.
the quotient of a number z and 2 is 7.

6. A SOLUTION of an equation with a variable is a number that produces a TRUE statement when it is substituted for the variable.
Tell whether 19 or 20 is a solution to the equation.
k – 8 = 12
(19) – 8 = 12
(20) – 8 = 12
11 ≠ 12
12 = 12
19 is NOT A SOLUTION
20 is a SOLUTION

7. SOLUTION– (9) – 2 = 6 k – 2 = 6 7 ≠ 6 54 = 54 6n = 54 6(9) = 54
when you substitute for a variable the solution can be either TRUE or FALSE.
Substitute 9 for each variable. Is 9 the solution for each equation?
(9) – 2 = 6
k – 2 = 6
NOT A
SOLUTION
7 ≠ 6
6n = 54
6(9) = 54
SOLUTION
54 = 54
SOLUTION
4 = 36/s
4 = 36/(9)
4 = 4

8. x + 8 = 12 16 – m = 2 20 = 5y v ÷ 8 = 8 Mental Math
When solving simple equations using mental math, think of the equation as a question.
x + 8 = 12
“What number plus 8 is equal to 12? “
x = 4
16 – m = 2
“16 minus what number is equal to 2? “
m = 14
20 = 5y
“20 is equal to 5 times what number? “
y = 4
v ÷ 8 = 8
“What number divided by 8 is equal to 8? “
v = 64

9. Objective solve equations using addition and subtraction
In your notebook, draw a picture of what an equation looks like to you. Explain why your picture is “like an equation.” Then use your picture to solve an equation of your own.

10. EQUATION – y – 8 = 12 22 = 14 + z 5 ÷ x = 30 11a = 121
mathematical sentence formed by placing an “=“ between two expressions
y – 8 = 12
22 = 14 + z
5 ÷ x = 30
11a = 121

11. Equation x
+ 7 = 10
Left side
Right side
‘x’ has to be 3 in order to make the equation balanced.
Like a scale, the left side and right side must be the same in order to be balanced!

12. Section 2.5 “Solving Equations Using Addition & Subtraction”
How can you get the “unknown” by itself?
m + 24 = -18
“Undo” the operation by using the INVERSE (opposite) operation to both sides of the equation.

13. Solving Addition Equations…
Isolate the variable! Get ‘m’ by itself.
m + 24 = -18
To get the ‘m’
by itself get rid of
“adding 24.”
–24
– 24
Do the opposite.
“Subtract 24.”
m = -42
Whatever you do to
one side of the equation
you must do the other side.
-18 – 24
-18 + (-24) “opp-opp”
-42

14. m = -42 m + 24 = -18 (-42) + 24 = -18 -18 = -18 Check Your Work!
-18 = -18
Are both sides equal?

15. Try It Out 1). (6) + 7 = 13 1). x + 7 = 13 2). -7 = 9 +(-16)
1). (6) + 7 = 13
2). -7 = 9 +(-16)
3). -3 = (-14)
4).(3.5) – 0.4 = 3.1
1). x + 7 = 13
2). -7 = 9 + h
3). -3 = x
4). f – 0.4 = 3.1

16. Solving Subtraction Equations…
Isolate the variable! Get ‘y’ by itself.
-13 = y –15
To get the ‘y’
by itself get rid of
“subtracting 15.”
+15
+15
Do the opposite.
“Add 15.”
2 = y
Whatever you do to
one side of the equation
you must do the other side.

17. 2 = y -13 = y – 15 -13 = (2) – 15 -13 = -13 Check Your Work!
Are both sides equal?

18. Try It Out 1). (4) - 7 = -3 1). t - 7 = -3 2). 6 = -3 + (9)
3). ¾ = (3¼)– 2½
4) = (5.5) - 7
1). t - 7 = -3
2). 6 = -3 + x
3). ¾ = r – 2½
4) = p - 7