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
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
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!
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
1. 245
2. 5
3. 9
4. 315
Find the value of z if 7z + 5 = 40
Answer Now
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
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
1. 30
2. 4
3. 100
4. 1.2
Find the value of z if
Answer Now
1375
m
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
1. 186
2. 51
3. 39
4. 174
Find the value of z if
Answer Now
902
6
t
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.
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
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
1. – 3
2.
3.
4. 3
What is the value of x if 3 – 4x = 18 + x?
1
3
1
3
Answer Now
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
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
What is the value of x if 3(x + 4) = 2(x – 1)?
Answer Now
1. -14
2. -13
3. 13
4. 14
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
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
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
What is the value of x if – 3 + 12x = 12x – 3?
1. 0
2. 4
3. No solutions
4. Infinite solutions
Answer Now
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