Transcript Solving Multi-Step Inequalities

3.4 Objective
The student will be able to:
solve two-step equations.
To solve two-step equations, undo the
operations by working backwards.
Ask yourself:
1. What is the first thing
we are doing to x?
2. What is the second
thing?
To undo these steps, do the opposite operations in opposite order.
Example 1: Solve this two step equation
1.
2.
3.
4.
5.
6.
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
1.
2.
3.
4.
5.
6.
2) 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
x
3) 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
4) Solve 3y – 1 = 8
1. y = 3
2. y = -3
7
3. y =
3
7
4. y =
3
Answer Now
5) 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 1
6) Solve
 6
3
1.
2.
3.
4.
d = -7
d = -19
d = -17
d = 17
Answer Now
1.
2.
3.
4.
a
7) Solve 3   2
7
-3
-3
a
  5
Draw “the river”
7
Subtract 3 from
a
both sides

7



5
Simplify
7
Clear the fraction
a = 35
– Multiply both
sides by -7
5. Simplify
6. Check your
answer
35
3
 2
7
3  5  2
7
8) Solve 5z + 16 = 51
1.
2.
3.
4.
z = -35
z = -7
z = 35
z=7
Answer Now
3x
1  4
9) 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