Download MultiStep Equations with Variables on Both Sides

Multi-Step Equations
Notes and Practice
Essential Question

How do I solve an equation that has more than
one variable term?
Multi-Step Equations

Equations will not always be able to be solved in
one or two steps.

You will see many more complicated equations in
higher math.
6 – x – 3 = 4(x – 2) + 4
Process

Simplify both sides of the equation separately

Add/subtract to get all variable terms to one side
of the equation (stay fair and balanced!)

Solve the remaining two-step equation
Example
2x – 5(x + 4) = -2
2x – 5x – 20 = -2
-3x – 20 = -2
+20 +20
-3x = 18
-3
-3
x = -6
Original problem
Distribute -5
Combine like terms
Add 20 to both sides
Divide both sides by -3
Example
3x  4  x  14 Original problem
+x
+x
4x + 4 = 14
-4 -4
4x = 10
4
4
x = 5/2
_
Add x to both sides
_
Subtract 4 from both sides
Divide both sides by 4
Practice (Be sure to check your answer!)
1) 5y – 7 = 3y – 13
2) 4(w + 1) – 2 = 18
3) 7x + 3 – 12 = -x + 7
4) 3(x – 2) = 12
5) 2x + 4 + 3x = 20 + x + 8
6) 9p + 27 – 3p = 72
Compare with a partner!
What about that original problem?
6 – x – 3 = 4(x – 2) + 4
6 – x – 3 = 4x – 8 + 4
-x + 3 = 4x – 4
3 = 5x – 4
7 = 5x
7/5 = x
x=
7
5
Essential Question

How do I solve an equation that has more than
one variable term?