3-1 Solving One-Step Equations
14
Solving equations means to get the variable by itself (isolate).
 Note: The answer should look like (variable) = (some number), where the variable is never negative
Solve using addition and subtraction.
r  16  7
1.
Get the variable by itself. Right now 16 is being added to it.
 16  16 Undo the addition by subtracting 16 from both sides.
r  23 Answer.
Subtraction Property
of Equality
Subtracting the same
value from both sides
of the equation.
Note: What ever you do to one side, you MUST do to the other side (keep it balanced).
2. x  2  3
3. 8  m  3
When solving equations, eliminate double signs.
As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”.
4. y  (3)  8
y 3  8
3 3
y  11
Addition Property of Equality
Adding the same value from both
sides of the equation.
5. p  (5)  6
6.  x  (2)  1
 x  2 1
2 2
 x  1 The opposite of x is -1. What is just x?
x 1
Solve using multiplication and division.
5t  60 Get the variable by itself. Right now -5 is being multiplied to it.
-5t 60

Undo the multiplication by dividing both sides by -5.
7.
-5
5
t  12 Answer.
Division Property
of Equality
Dividing the same
value from both sides
of the equation.
Remember: What ever you do to one side, you MUST do to the other side (keep it balanced).
8. 15  6n
9. 3 y  129
x
 12 Since 4 is dividing x, multiply both sides by 4 to clear the fraction.
4
x
Multiplication
(4)  12(4)
Property
of Equality
4
Multiplying the same
4x
4x
 48
The fours will cancel each other out.
simplifies to 1x
value from both sides
4
4
of the equation.
x  48
10.
2
x  18 To get rid of multiplying a fraction, multiply by the reciprocal.
3
32
 3
  x  18   Multiply straight across.
23
 2
54
x
2
x  27
11.
Inverse Operations
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Inverse Operations “UNDO” Each Other!
Try these on your own.
1. p – (-27) = 13
2. -7 = -16 – k
3.

2
t  10
5
15
Algebra 1 Homework: 3.1 Solving One-Step Equations
Solve the Equation. (Write the Steps!)
1. x + 2 = 10
2. 3x = -15
3. -4 + x = 12
4.
x
3
= -6
5. 15 = t – 2
6.
1
x
2
=3
7. x – (-4) = 3
8. 3 = -x
9. w + 14 = -8
10. y + (-10) = 6
11. -11 = a + 8
12. 5h = 35
13. -2.3 = x + (-1.1)
14. -7 = -16 - k
15. -13m = 39
16. z + (-13) = -27
17. p - (-27) = 13
18. 41 = 32 - r
19.
2
X  16
3
1
2
20.  X 
2
3