solve two-step equations solve equations with variables on both sides
DESCRIPTION
Objectives The student will be able to:. Solve two-step equations Solve equations with variables on both sides Solve equations containing grouping symbols. Adapted from original designed by Skip Tyler, Varina High School. Solve: 8x + 5 = 61. Step 1. Step 2. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/1.jpg)
1. Solve two-step equations
2. Solve equations with variables on both sides
3. Solve equations containing grouping symbols.
ObjectivesThe student will be able to:
Adapted from original designed by Skip Tyler, Varina High School
![Page 2: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/2.jpg)
Solve: 8x + 5 = 61
Step 1
Examine the problem
Figure out the order that you would DO to solve if you knew the value of the variable.
Use PEMDAS!
Step 2
Completely UNDO those steps
Working in reverse order using inverse operations!
![Page 3: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/3.jpg)
Solve: 8x + 5 = 61 – 5 – 5
8x = 56
x = 7
8(7) + 5 = 61
56 + 5 = 61
1. Draw “the river”2. Subtract 5 from
both sides3. Simplify4. Divide both sides
by 85. Simplify
6. Check your answer
8 8
![Page 4: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/4.jpg)
1. 245
2. 5
3. 9
4. 315
Find the value of z if 7z + 5 = 40
Answer Now
![Page 5: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/5.jpg)
Solve:
+ 9 + 9
= 40
a = −160
40 − 9 = 31
1. Draw “the river”2. Add 9 to both
sides3. Simplify4. Multiply both
sides by -45. Simplify
6. Check your answer
3194
a
4a
3194
160
−4 −4
![Page 6: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/6.jpg)
Solve:
− 8 − 8
= − 20
y = −80
−20 + 8 = −12
1. Draw “the river”2. Subtract 8 from
both sides3. Simplify4. Multiply both
sides by 45. Simplify
6. Check your answer
1284
y
4
y
1284
80
4 4
![Page 7: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/7.jpg)
1. 30
2. 4
3. 100
4. 1.2
Find the value of z if
Answer Now
1375
m
![Page 8: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/8.jpg)
Solve:
= (4)3
m – 8 = 12 + 8 = + 8
m = 20
12/3 = 4
1. Draw “the river”2. Multiply both
sides by 33. Simplify4. Add 8 to both
sides 5. Simplify
6. Check your answer
43
8
m
3
83
m
43
820
![Page 9: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/9.jpg)
1. 186
2. 51
3. 39
4. 174
Find the value of z if
Answer Now
902
6
t
![Page 10: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/10.jpg)
Solve: 3x + 2 = 4x – 1
You need to get the variables on one side of the equation.
It does not matter which variable you move.
Try to move the one that will keep your variable positive.
![Page 11: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/11.jpg)
Solve: 3x + 2 = 4x – 1
- 3x - 3x
2 = x – 1
+ 1 + 1
3 = x
3(3) + 2 = 4(3) – 1
9 + 2 = 12 – 1
1. Draw “the river”2. Subtract 3x from
both sides3. Simplify4. Add 1 to both
sides5. Simplify
6. Check your answer
![Page 12: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/12.jpg)
Solve: 8y – 9 = –3y + 2 + 3y + 3y
11y – 9 = 2
+ 9 + 9
11y = 11
11 11
y = 1
8(1) – 9 = –3(1) + 2
1. Draw “the river”2. Add 3y to both sides3. Simplify4. Add 9 to both sides5. Simplify6. Divide both sides by
117. Simplify
8. Check your answer
![Page 13: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/13.jpg)
1. – 3
2.
3.
4. 3
What is the value of x if 3 – 4x = 18 + x?
1
3
1
3
Answer Now
![Page 14: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/14.jpg)
Solve: 4 = 7x – 3x 4 = 4x
4 4
1 = x
4 = 7(1) – 3(1)
1. Draw “the river” – Notice the variables
are on the same side!2. Combine like terms3. Divide both sides by 44. Simplify5. Check your answer
![Page 15: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/15.jpg)
Solve: – 7(x – 3) = – 7
– 7x + 21 = – 7
– 21 – 21
– 7x = – 28
– 7 – 7
x = 4
– 7(4 – 3) = – 7
– 7(1) = – 7
1. Draw “the river” 2. Distribute3. Subtract 21 from both
sides4. Simplify5. Divide both sides by -76. Simplify
7. Check your answer
![Page 16: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/16.jpg)
What is the value of x if 3(x + 4) = 2(x – 1)?
Answer Now
1. -14
2. -13
3. 13
4. 14
![Page 17: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/17.jpg)
3 - 2x = 4x – 6
+ 2x +2x
3 = 6x – 6
+ 6 + 6
9 = 6x
6 6
or 1.5 = x
Solve:
1. Draw “the river”2. Clear the fraction – multiply
each term by the LCD3. Simplify4. Add 2x to both sides5. Simplify6. Add 6 to both sides7. Simplify8. Divide both sides by 69. Simplify
10. Check your answer
3
8
1
4x
1
2x
3
4
(8)3
8 (8)
1
4x (8)
1
2x (8)
3
4
1.53 1 1 3
8 4 2 41.5
3
2
![Page 18: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/18.jpg)
Special Case #1 6) 2x + 5 = 2x – 3
– 2x – 2x
5 = – 3
1. Draw “the river” 2. Subtract 2x from both
sides3. Simplify
This is never true!
No solutions
![Page 19: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/19.jpg)
Special Case #2 3(x + 1) – 5 = 3x – 2
3x + 3 – 5 = 3x – 2
3x – 2 = 3x – 2
– 3x – 3x
– 2 = – 2
1. Draw “the river” 2. Distribute3. Combine like terms4. Subtract 3x from both
sides5. Simplify
This is always true!
Infinite solutions or identity
![Page 20: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/20.jpg)
What is the value of x if – 3 + 12x = 12x – 3?
1. 0
2. 4
3. No solutions
4. Infinite solutions
Answer Now
![Page 21: Solve two-step equations Solve equations with variables on both sides](https://reader036.vdocuments.mx/reader036/viewer/2022062518/56814314550346895daf6896/html5/thumbnails/21.jpg)
1. -8
2. -2
3. 2
4. 8
Challenge! What is the value of x if – 8(x + 1) + 3(x – 2) = – 3x + 2?
Answer Now