Post on 05-Jan-2016
3.1
Solving 2-step equations
3.1 – Solving 2-step Equations
Goals / “I can…”Solve 2-step equationsUse deductive reasoning
3.1 – Solving 2-step Equations
When looking at an algebraic equation like
x + 7 = 15we 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
½ x = 9we 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.
Example:
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
3 72
x
To undo these steps, do the opposite operations in opposite order.
1. Draw “the river”2. Add 3 to both sides3. Simplify4. Clear the fraction -Multiply
both sides by 25. Simplify6. Check your answer
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
Follow the steps in the ‘undo’ column to isolate the variable.
3 72
x
+ 3 + 3
= - 4
x = -8
-4 – 3 = -7
2
x
+3
· 22 · · 2
38
72
1) Solve 2x - 1 = -3
+ 1 + 1
2x = -2
2 2
x = -1
2(-1) - 1 = -3
-2 – 1 = -3
1. Draw “the river”2. Add 1 to both
sides3. Simplify4. Divide both sides
by 25. Simplify6. Check your
answer
D U· 2- 1
+ 1÷ 2
+ 4 + 4
3 · · 3
x = 36
12 – 4 = 8
123
x
2) Solve 4 83
x
1. Draw “the river”2. Add 4 to both
sides3. Simplify4. Clear the fraction
-Multiply both sides by 3
5. Simplify6. Check your
answer
D U÷ 3- 4
+ 4· 3
364 8
3
3) Solve 3y – 1 = 8
7
3
1. y = 3
2. y = -3
3. y =
4. y = 7
3
Answer Now
3) Solve d 4
23
d – 4 = 6
+ 4 + 4
d = 10
1. Draw “the river”2. Clear the fraction
- Multiply both sides by 2
3. Simplify4. Add 4 to both
sides5. Simplify6. Check your
answer
D U- 4÷ 2
· 2+ 4
42 3 2
2
d
10 43
2
4) Solve1
63
d
1. d = -7
2. d = -19
3. d = -17
4. d = 17
Answer Now
5) Solve 3 27
a
-3 -3
a = 35
1. Draw “the river”2. Subtract 3 from
both sides3. Simplify4. Clear the fraction
– Multiply both sides by -7
5. Simplify6. Check your
answer
D U÷ -7+ 3
- 3· -7
Do/Undo Chart – This one is tricky! Remember to always use the sign in
front of the number.
57
a
7 5 77
a
3 235
7
3 5 2
6) Solve 5z + 16 = 51
1. z = -35
2. z = -7
3. z = 35
4. z = 7
Answer Now
- 1 - 1
5 · · 5
3x = 15
3 3
x = 5
7) Solve 3
1 45
x
1. Draw “the river”2. Subtract 1 from both
sides3. Simplify4. Clear the fraction -
Multiply both sides by 5
5. Simplify6. Divide both sides by 37. Simplify8. Check your answer
D U· 3 ÷ 5+ 1
- 1· 5÷ 3
33
5
x
3( )1 4
5
5
3.1 – Solving 2-step Equations
A music store sells a copycopy 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?