what is a two-step equation? an equation written in the form ax + b = c
TRANSCRIPT
![Page 1: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/1.jpg)
Solving Two-Step Equations
![Page 2: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/2.jpg)
What is a Two-Step Equation?
An equation written in the form
Ax + B = C
![Page 3: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/3.jpg)
a) 3x – 5 = 16
b) y/4 + 3 = 12
c) 5n + 4 = 6
d) n/2 – 6 = 4
Examples of Two-Step Equations
![Page 4: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/4.jpg)
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…
![Page 5: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/5.jpg)
Addition Subtraction
Opposite Operations
Multiplication Division
![Page 6: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/6.jpg)
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?
![Page 7: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/7.jpg)
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
![Page 8: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/8.jpg)
2x – 5 = 17
3y + 7 = 25
Try These Examples
5n – 2 = 38
12b + 4 = 28
![Page 9: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/9.jpg)
x = 11
y = 6
Check your answers!!!
n = 8
b = 2
![Page 10: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/10.jpg)
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
![Page 11: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/11.jpg)
x 5 – 3 = 8
c 7 + 4 = 9
Try these examples!
r 3 – 6 = 2
d 9 + 4 = 5
![Page 12: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/12.jpg)
x = 55
c = 35
Check your answers!!!
r = 24
d = 9
![Page 13: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/13.jpg)
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!
![Page 14: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/14.jpg)
Wait! There’s more…
![Page 15: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/15.jpg)
Solving Multi-Step Equations
![Page 16: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/16.jpg)
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.
![Page 17: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/17.jpg)
a) 8x - 3x - 10 = 20
b) 7x + 2(x + 6) = 39
c) (3x + 5) = -24
Examples of Multi-Step Equations
3
2
![Page 18: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/18.jpg)
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
![Page 19: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/19.jpg)
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
![Page 20: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/20.jpg)
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
![Page 21: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/21.jpg)
(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
![Page 22: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/22.jpg)
12v + 14 + 10v = 80
3 + 4(z + 5) = 31
Try these examples!
5h + 2(11 – h) = -5
(3/2)(x – 5) = -6
![Page 23: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/23.jpg)
v = 3
z = 2
Check your answers!!!
h = -9
x = 1
![Page 24: What is a Two-Step Equation? An equation written in the form Ax + B = C](https://reader036.vdocument.in/reader036/viewer/2022062304/56649d955503460f94a7e165/html5/thumbnails/24.jpg)
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