what is a two-step equation? an equation written in the form ax + b = c
TRANSCRIPT
Solving Two-Step Equations
What is a Two-Step Equation?
An equation written in the form
Ax + B = C
a) 3x – 5 = 16
b) y/4 + 3 = 12
c) 5n + 4 = 6
d) n/2 – 6 = 4
Examples of Two-Step Equations
1. Solve for any Addition or Subtraction on
the variable side of equation by “undoing”
the operation from both sides of the
equation.
2. Solve any Multiplication or Division from
variable side of equation by “undoing” the
operation from both sides of the equation.
Steps for Solving Two-Step Equations
PEMDAS in Reverse…
Addition Subtraction
Opposite Operations
Multiplication Division
Identify what operations are on the variable
side. (Add, Sub, Mult, Div)
“Undo” each operation by using the
opposite operation.
Whatever you do to one side, you must do
to the other side to keep the equation
balanced.
Helpful Hints?
4x – 5 = 11
+5 = +5 (Add 5 to both sides)
4x = 16 (Simplify)
4 = 4 (Divide both sides by 4)
x = 4 (Simplify)
Ex. 1: Solve 4x – 5 = 11
2x – 5 = 17
3y + 7 = 25
Try These Examples
5n – 2 = 38
12b + 4 = 28
x = 11
y = 6
Check your answers!!!
n = 8
b = 2
x 3 + 4 = 9
- 4 = - 4 (Subtract 4 from both sides)
x 3 = 5 (Simplify)
(x 3) 3 = 5 3 (Multiply by 3 on both sides)
x = 15 (Simplify)
Ex. 2: Solve x 3 + 4 = 9
x 5 – 3 = 8
c 7 + 4 = 9
Try these examples!
r 3 – 6 = 2
d 9 + 4 = 5
x = 55
c = 35
Check your answers!!!
r = 24
d = 9
1. Make sure your equation is in the form
Ax + B = C
2. Keep the equation balanced.
3. Use opposite operations to “undo”
Follow the rules (PEMDAS in Reverse):
1. Undo Addition or Subtraction
2. Undo Multiplication or Division
Time to Review!
Wait! There’s more…
Solving Multi-Step Equations
What is a Multi-Step Equation?A multi-step equations takes more than two steps to solve.
The same rules for two-step equations apply, but now you have equations that require you to do additional work BEFORE you begin to isolate the variable.
a) 8x - 3x - 10 = 20
b) 7x + 2(x + 6) = 39
c) (3x + 5) = -24
Examples of Multi-Step Equations
3
2
1. Start by simplifying one or both sides of the
equation. This may require:
a. Combining like terms
b. Using the distributive property
c. Multiplying by a reciprocal
2. Use inverse operations (PEMDAS in
reverse) to isolate the variable.
Steps for Solving Multi-Step Equations
8x – 3x – 10 = 20 Original equation
5x – 10 = 20 Combine like terms
+10 = +10 Add 10 to both sides
5x = 30 Simplify
5 = 5 Divide both sides by 5
x = 6 Simplify
Ex 1: 8x - 3x - 10 = 20
7x + 2(x + 6) = 39 Original equation
7x + 2x + 12 = 39 Distributive property
9x + 12 = 39 Combine like terms
-12 = -12 Subtract 12 from both sides
9x = 27 Simplify
9 = 9 Divide both sides by 9
x = 3 Simplify
Ex 2: 7x + 2(x + 6) = 39
(3/2)(3x + 5) = -24 Original equation
·(2/3) = ·(2/3) Multiply by reciprocal
3x + 5 = -16 Simplify (-24/1 * 2/3 = -48/3 = -16)
-5 = -5 Subtract 5 from both sides
3x = -21 Simplify
3 = 3 Divide both sides by 3
x = -7 Simplify
Ex 3: (3x + 5) = -24 3
2
12v + 14 + 10v = 80
3 + 4(z + 5) = 31
Try these examples!
5h + 2(11 – h) = -5
(3/2)(x – 5) = -6
v = 3
z = 2
Check your answers!!!
h = -9
x = 1
TB pp. 144-145 #1, 3, 7, 11, 15, 19, 21, 22, 25, 27, 31, 35, 40
TB pp. 150-151 #1, 5, 11, 13, 17, 18, 19, 23, 27, 31
Homework