Transcript Solving Two-Step Inequalities

Objective
The student will be able to:
solve two-step inequalities.
1.
2.
3.
4.
5.
6.
7.
1) Solve 5m - 8 > 12
Draw a wall
+8 +8
Add 8 to both sides
5m
> 20
Simplify
Divide both sides by 5
5
5
Simplify
Check your answer
m>4
Graph the solution
5(4) – 8 = 12
3
o
4
5
1.
2.
3.
4.
5.
2) Solve 12 - 3a > 18
Draw a wall
- 12
- 12
Subtract 12 from both
-3a > 6
sides
Simplify
-3 -3
Divide both sides by -3
Simplify
a
<
-2
(Switch the inequality!)
Check your answer
12 - 3(-2) = 18
6.
7. Graph the solution
-3
o
-2
-1
Which graph shows the solution to
2x - 10 ≥ 4?
1.
.
2.
3.
4.
Answer Now
3) Solve 5m - 4 < 2m + 11
1. Draw a wall
2. Subtract 2m from both
sides
3. Simplify
4. Add 4 to both sides
5. Simplify
6. Divide both sides by 3
7. Simplify
8. Check your answer
9. Graph the solution
4
-2m
-2m
3m - 4 < 11
+4 +4
3m < 15
3
3
m<5
5(5) – 4 = 2(5) + 11
o
5
6
4) Solve 2r - 18 ≤ 5r + 3
-2r
1.
2.
3.
4.
5.
6.
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8.
9.
Draw a wall
Subtract 2r from both sides
Simplify
Subtract 3 from both sides
Simplify
Divide both sides by 3
Simplify
Check your answer
Graph the solution
-8
-2r
-18 ≤ 3r + 3
-3
-3
-21 ≤ 3r
3
3
-7 ≤ r or r ≥ -7
2(-7) – 18 = 5(-7) + 3
●
-7
-6
6) Solve -2x + 6 ≥ 3x - 4
1.
2.
3.
4.
x>
x<
x>
x<
-2
-2
2
2
Answer Now
5) Solve
1.
2.
3.
4.
5.
6.
7.
8.
9.
Draw a wall
Subtract 14p from both
sides
Simplify
Add 20 to both sides
Simplify
Divide both sides by 12
Simplify
Check your answer
Graph the solution
6
26p - 20 > 14p + 64
-14p
-14p
12p – 20 > 64
+ 20 + 20
12p > 84
12
12
p>7
26(7) – 20 = 14(7) + 64
o
7
8
What are the values of x if
3(x + 4) - 5(x - 1) < 5?
1.
2.
3.
4.
x < -6
x > -6
x<6
x>6
Answer Now
Solve
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3(x + 4) - 5(x - 1) < 5
3x
+12
5x
+
5
<
5
Draw a wall
Distribute first
17 – 2x < 5
Combine like terms
-17
-17
Subtract 17 from both sides
Simplify
- 2x <-12
Divide both sides by -2
Do you need to change the
-2
-2
inequality sign? Yes!
x>6
Simplify
Check your answer
3(6
+
4)
-5(6
-1)
=
5
Graph the solution
o
6
7
8