Download Solve Absolute Value Inequalities Solve Absolute Value Inequalities

Solve for x.
1. 3𝑥 + 1 = 8
2. 3 𝑥 − 2 = 4
3. −2 𝑥 = 10
1.
3𝑥 + 1 = 8
3x + 1 = 8
or 3x + 1 = - 8
-1
-1
-1
-1
3x = 7
3x = -9
3
3
3
3
x=
7
3
or x = -3
2. 3 𝑥 − 2 = 4
+2 +2
3𝑥 =6
3
3
𝑥 =2
x = 2 or x = -2
3. −2 𝑥 = 10
-2
-2
𝑥 = −5
No Solution
Algebra II
 To
write & solve inequalities
involving absolute value
 Less
Th”AND”
𝑥 <5
x < 5 AND
 Great”OR”
𝑥 >5
x > 5 OR
x > -5
Flip
Inequality
& Change
Sign!
x < -5
1.
2𝑥 − 1 < 5
Less ThAND
2x – 1 < 5
and 2x
+1 +1
2x < 6
2x
2
2
2
x < 6 and x > -2
–1>-5
+1
+1
> -4
2
-2 < x < 6
2.
3𝑥 − 4 ≤ 8
Less ThAND
3x - 4 ≤ 8
and 3x – 4 ≥ -8
+4 +4
+4 +4
3x ≤ 12
3x ≥ -4
3
3
3
3
x ≤ 4 and x ≥
4
−
3
4
−
3
≤x≤4
3.
2𝑥 + 4 ≥ 6
GreatOR
2x + 4 ≥ 6 or
2x + 4 ≤-6
-4 -4
- 4 -4
2x ≥ 2
2x ≤ -10
2
2
2
2
x ≥ 1 or x ≤ -5
4.
5𝑥 + 10 > 25
GreatOR
5x + 10 > 25 or 5x + 10 < -25
- 10 -10
-10 -10
5x > 15
5x < -35
5
5
5
5
x > 3 or x < -7
5.
−2𝑥 + 3 > -4
All Real Numbers
Absolute Value is always positive &
will ALWAYS be greater than a
negative number!!
6.
−3𝑥 + 4 < −12
No Solution
Absolute Value is always positive &
will NEVER be less than a negative
number!!
7.
* Know it’s Great“or” >
𝑥−# >#
* Find average of endpoints
−1 + 11 10
=
=5
2
2
*Find how far endpts are from avg: 6
𝑥−5 >6
8.
* Know it’s LessAnd or Equal to ≤
𝑥−# ≤#
* Find average of endpoints
−8 + 12 4
= =2
2
2
*Find how far endpts are from avg: 10
𝑥 − 2 ≤10
9.
* Know it’s Great“or” or equal to ≥
𝑥−# ≥#
* Find average of endpoints
−10 + 6 −4
=
= −2
2
2
*Find how far endpts are from avg: 8
𝑥 − (−2) ≥ 8
𝑥+2 ≥8
10.
* Know it’s LessAnd <
𝑥−# <#
* Find average of endpoints
−3 + 3 0
= =0
2
2
*Find how far endpts are from avg: 3
𝑥−0 <3
𝑥 <3
 Your
friend show the problem as
shown. Describe and correct the
error.