1. Objective - To solve simple, one-step variable equations
What is an equation?
Equation - a balanced statement of equality
between two quantities.
4 + 3 = 7
4 + 3 7 =
fulcrum

2. 4 + 3 7 =
- 3
fulcrum

3. 4 = 7
fulcrum

4. 4 = 7
fulcrum

5. 4 = 7
fulcrum

6. 4 + 3 7 =
- 3
- 3

7. 4 4 = Perform the same operation to both sides
to keep the equation balanced.

8. This property can be used to solve variable equations.
x + 6 11 = -6 -6 x 5 =
Algebraic Approach
x + 6 = 11
x = 5

9. Solve.
1) m + 2 = 10
4) m - 4 = 9
m = 8
m = 13
2) x - 4 = 6
5) 11 = x - -2
x = 10
9 = x
3) x + 7 = 3
6) 8 + y = -6
x = -4
y = -14

10. Linear vs. Non-linear
Linear Equations
Non-linear Equations

11. Rules for Solving Linear Equations
1) Goal: Isolate the variable.
2) Undo operations with their opposite operation.
3) Always do the same thing to both sides of the equation.

12. Solve.
1) -4 + x = 15
4) - 4 = m + 9
x = 19
-13 = m
2) 7 = x + 13
5) = x
16 = x
-6 = x
3) -10 = 6 + x
6) y =
y = -5
-16 = x

13. Solve.
1) 5x = 35
3) 9 = -3m
x = 7
-3 = m 2) 4)
(-6)
(-6)
-72 = x

14. Storyboard your Problem
-4 + x = 15
x = 15
A number is 20
Add Add 4 Is

15. -4k = 14 -4 -4 Acceptable Answers All answers must be fully reduced!
All answers must be fully reduced!
There is nothing improper about an improper fraction!

16. Solve.
1) 7x = 16
3) 9 = -m
(-1)9 = -m(-1)
-9 = m 2) 4)
(-4)
(-4)
(-2)
(-2)
k = 16

17. Solving Equations Involving Fractions
Long Way
Short Way
Easier to multiply
by the reciprocal!

18. Solve. 1) 3) 2) 4)