Transcript Solving Multi-Step Inequalities

Objective
The student will be able to:
solve two-step equations.
SOL: A.1, A.3
Designed by Skip Tyler, Varina High School
To solve two-step equations, undo the
operations by working backwards.
Example:
x
 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.
Follow the steps in 5.
the ‘undo’
6.
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.
2.
3.
4.
5.
6.
1) Solve 2x - 1 = -3
+1 +1
Draw “the river”
2x = -2
Add 1 to both
sides
2
2
Simplify
Divide both sides
x
=
-1
by 2
Simplify
2(-1) - 1 = -3
Check your
answer
-2 – 1 = -3
·2
-1
+1
÷2
x
2) Solve  4  8
3
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
+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
a
5) Solve 3   2
7
Do/Undo Chart – This one is
-3
-3
tricky! Remember to always use
the sign in front of the number.
a
  5
1. Draw “the river”
7
2. Subtract 3 from
a
both sides

7



5
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
D
U
÷ -7 - 3
+ 3 · -7
7
6) Solve 5z + 16 = 51
1.
2.
3.
4.
z = -35
z = -7
z = 35
z=7
Answer Now
3x
1  4
7) Solve
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
÷5
+1
-1
·5
÷3