Transcript 3.1 - Welcome to Lawton Community Schools

3.1
Solving 2-step equations
3.1 – Solving 2-step Equations
Goals / “I can…”
Solve 2-step equations
Use deductive reasoning
3.1 – Solving 2-step Equations
 When looking at an algebraic equation like
x + 7 = 15
 we try to figure out how to get x by itself. We
must get rid of the +7. To do this, we might
say we undo the + 7 or do the opposite of +
7. Either way we could – 7 from both sides.
x + 7 = 15
-7 -7
x=8
3.1 – Solving 2-step Equations
When looking at an algebraic equation
like
½x=9
we try to get x by itself. We must get
rid of the multiply by ½ by doing the
inverse of that which is to multiply by
the reciprocal or 2.
2(½ x) = (9)2
x = 18
To solve two-step equations, undo the
operations by working backwards.
x
Example:
 3  7
2
Ask yourself,
1. What is the first
thing we are doing
to x?
2. What is the second
thing?
Recall the order of
operations as you
answer these
questions.
• Dividing by 2
• Subtracting 3
To undo these steps, do the opposite operations in opposite order.
Use a DO-UNDO chart as a shortcut to
answering the questions.
In the table, write the opposite operations in the opposite
order
DO UNDO
÷2 +3
-3 · 2
1.
2.
3.
4.
5.
6.
Follow the steps
in the ‘undo’
column to
isolate the
variable.
Draw “the river”
Add 3 to both sides
Simplify
Clear the fraction -Multiply
both sides by 2
Simplify
Check your answer
x
 3  7
2
+3
+3
x
2·
= - 4· 2
2
x = -8
8
 3  7
2
-4 – 3 = -7
D U
1) Solve 2x - 1 = -3
1. Draw “the river”
2. Add 1 to both
sides
3. Simplify
4. Divide both
sides by 2
5. Simplify
6. Check your
answer
+1 +1
2x = -2
2
2
x = -1
2(-1) - 1 = -3
-2 – 1 = -3
·2
-1
+1
÷2
2) Solve
1. Draw “the river”
2. Add 4 to both
sides
3. Simplify
4. Clear the
fraction -Multiply
both sides by 3
5. Simplify
6. Check your
answer
x
48
3
+4 +4
x
3 ·  12· 3
3
x = 36
36
48
3
12 – 4 = 8
D U
÷3 +4
- 4 ·3
3) Solve 3y – 1 = 8
1. y = 3
2. y = -3
7
3. y =
3
7
4. y =
3
Answer Now
3) Solve
1. Draw “the river”
2. Clear the fraction
- Multiply both
sides by 2
3. Simplify
4. Add 4 to both
sides
5. Simplify
6. Check your
answer
2
d4
3
2
d 4
3 2
2
d–4= 6
+4 +4
d = 10
10  4
3
2
D
U
-4
÷2
·2
+4
d 1
4) Solve
 6
3
1.
2.
3.
4.
d = -7
d = -19
d = -17
d = 17
Answer Now
D
a
÷ -7
3



2
5) Solve
+3
7
Do/Undo Chart – This one is tricky!
Remember to always use the sign in
-3
-3
front of the number.
a
  5
1. Draw “the river”
7
2. Subtract 3 from
a
both sides

7



5

7
3. Simplify
7
4. Clear the fraction
a = 35
– Multiply both
sides by -7
5. Simplify
6. Check your
answer
35
3
 2
7
3  5  2
U
-3
· -7
6) Solve 5z + 16 = 51
1.
2.
3.
4.
z = -35
z = -7
z = 35
z=7
Answer Now
3x
7) Solve
1  4
5
-1 -1
1.
2.
3.
4.
5.
6.
7.
8.
Draw “the river”
Subtract 1 from both
sides
Simplify
Clear the fraction Multiply both sides by
5
Simplify
Divide both sides by 3
Simplify
Check your answer
3x
3 · 5
5·
5
3x = 15
3
3
x=5
3(5)
1  4
5
D U
·3 -1
÷5 ·5
+1 ÷3
3.1 – Solving 2-step Equations
A music store sells a copy of a deluxe
electric guitar for $295. This is $30 more
than 1/3 the cost of the deluxe electric
guitar it is modeled after. What is the cost
of the deluxe guitar?