1. 10/3/11 In your notebook, answer completely the following:
Draw a picture of what an equation looks like to you. Then use your picture to solve an equation of your own.

2. Objective
solve one-step equations using algebra

3. Equation- mathematical sentence with an equal sign both sides
Like a scale,
both sides
must be balanced

4. Addition and Subtraction Properties of Equality
Solving an Equation
How can you get the “unknown” by itself?
Addition and Subtraction Properties of Equality
Adding or subtracting both sides of the equation by the same nonzero number produces an EQUIVALENT EQUATION.
“Undo” the operation by using the INVERSE (opposite) operation to both sides of the equation.

5. 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.

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

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

8. 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.

9. -13 = y - 15 2 = y -13 = (2) - 15 Check Your Work!
Are both sides equal?

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

11. Multiplication and Division Properties of Equality
Solving an Equation
How can you get the “unknown” by itself?
Multiplication and Division Properties of Equality
Multiplying or dividing both sides of the equation by the same nonzero number produces an EQUIVALENT EQUATION.
“Undo” the operation by using the INVERSE (opposite) operation to both sides of the equation.

12. Solving a Multiplication Equation
-2y = 28
“Undo” multiplication by dividing both sides of the equation
y = -14

13. Check Your Work!
-2y = 28
y = -14
-2(-14) = 28
Are both sides equal?

14. Try It Out 1). -7(-9) = 63 1). -7t = 63 2). -144 = 12(-12)
1). -7(-9) = 63
2) = 12(-12)
3). 10(1/2) = 5
4) (4.67)= -7
1). -7t = 63
2) = 12d
3). 10x = 5
4) g = -7

15. Solving a Division Equation
5· · 5
j =
“Undo” division by multiplying both sides of the equation
j = -35

16. Check Your Work!
j = -7 5
j = -35
-35 =
Are both sides equal?

17. Try It Out 1). r ÷ 8 = -2 2). v = 8 4 3). 9 = a 5 4). e/-7= -2
1). -16 ÷ 8 = -2
2). 32 =
3). 9 =
4). 14/-7 = -2

18. Find the width of the rectangle.x
Area = 38 cm² 2
z = 3
x = 19 9
Area = 27 m² z

19. Solving a Two-Step Equation
How can you get the “unknown” by itself?
3x + 5 = -19
“Undo” operations by using the INVERSE (opposite) operation to both sides of the equation.
Solving Two-Step Equations
STEP 1- “Undo” addition and/or subtraction.
STEP 2- “Undo” multiplication and/or division.
STEP 3- Solve for the variable.
STEP 4- Check your work.

20. Solving Two-Step Equations…
Isolate the variable! Get ‘x’ by itself.
3x + 5 = -19
To get the ‘x’ by
itself first get rid
of “adding 5.” 5 5
Do the opposite.
“Subtract 5.”
Whatever you do to
one side of the equation
you must do the other side.
3x = -24
To get the ‘x’ by
itself get rid
of “multiplying by 3.” 3 3
Do the opposite.
“Divide by 3.”
x = -8

21. 3x + 5 = -19 x = -8 3(-8) + 5 = -19 Check Your Work!
Are both sides equal?