Download Solve Multi-step Equations (var. both sides)

Solve Multi-step Equations
(var. both sides)
Students will solve multi-step
equations with variables on
both sides using distributive
property, combining like terms,
and inverse operations.
1
b  7  3(b  4)  3
2
To solve equations with variables
on both sides…
Simplify each side of the equation separately using
Distributive Property and
Combining Like Terms.
Use Inverse Operations to move the term with the
variable to the left side of the equation.
Use Inverse Operations to solve the equations.
Solve: 5x + 3 = 2x + 15
–2x
–2x
Use Inverse Operations
to move the variable to
the left side.
3x + 3 = 15
–3 –3
3x = 12
3
3
x=4
Check: 5(4) + 3 = 2(4) + 15
8 + 15
20 + 3
23
23

Simplify Each Side of the Equation and
Solve
x–4–2=8–(9+x)
C.L.T.
Use Inverse
Operations to
move the variable
to the left side.
x –6
= 8 –9 –x
Distributive
Property
C.L.T.
x – 6 = -1 – x
+x
+x
Add x to both sides
2x – 6 = -1
Add 6 to both sides
+6 +6
2x = 5
Divide both sides by 2
2 2
Leave the answer as
5
an improper fraction.
x 
2
Solve: -3x – x = -2x + 7 – 2x
-4x = - 4x + 7
+4x
+4x
0 = 7
?
0 is NEVER
equal to 7…
That means
“NO
SOLUTION”
Nothing will make the equation true.
Solve: 3 ( 2x – 5 ) = 6x – 15
6x – 15 = 6x – 15
−6x
−6x
- 15 = - 15
If the numbers are
equal, that
means…
“All Real Numbers”
Any number will make the equation true.
Handout: Solve Multi-step
Equations
1. Use distributive property and combine like
terms to simplify each side of the equations
separately.
2. Use inverse operation to move the variable
to the front (left) side of the equation.
3. Solve the remaining equation by using
inverse operations.
STOP