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Solve the compound inequality:
6
≤
2
x
−
8
<
10
6 \leq 2 x-8<10
6
≤
2
x
−
8
<
10
.
\newline
Enter the exact answer in interval notation.
\newline
To enter
∞
\infty
∞
, type infinity. To enter
∪
\cup
∪
, type U.
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Math Problems
Precalculus
Solve higher-degree inequalities
Full solution
Q.
Solve the compound inequality:
6
≤
2
x
−
8
<
10
6 \leq 2 x-8<10
6
≤
2
x
−
8
<
10
.
\newline
Enter the exact answer in interval notation.
\newline
To enter
∞
\infty
∞
, type infinity. To enter
∪
\cup
∪
, type U.
Isolate x:
Step
1
1
1
: Isolate x in the inequality
6
≤
2
x
−
8
<
10
6 \leq 2x - 8 < 10
6
≤
2
x
−
8
<
10
.
Divide by
2
2
2
:
Step
2
2
2
: Divide all parts of the inequality by
2
2
2
to solve for
x
x
x
.
Interval Notation:
Step
3
3
3
: Write the solution in interval notation.
More problems from Solve higher-degree inequalities
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Solve for
x
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\newline
3
(
x
+
2
)
(
x
+
5
)
>
0
3(x+2)(x+5) > 0
3
(
x
+
2
)
(
x
+
5
)
>
0
\newline
Write the solution using interval notation. Use the union symbol
∪
\cup
∪
to express the solution as a union of disjoint intervals. Finite endpoints of all intervals should be integers. If there are no solutions, use the symbol
∅
\varnothing
∅
for the empty set. Use the set notation
{
a
}
\{a\}
{
a
}
to represent an isolated solution
a
a
a
.
\newline
□
\square
□
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Solve the equation. Check your solution.
\newline
1
4
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−
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k
+
52
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=
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+
10
k
\frac{1}{4}(-16 k+52)=8+10 k
4
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k
\newline
The solution set is \{\} . Type an integer or a simp
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Posted 2 months ago
Question
Solve:
\newline
4
x
−
2
x
−
1
≤
3
\frac{4 x-2}{x-1} \leq 3
x
−
1
4
x
−
2
≤
3
\newline
x
∈
x \in
x
∈
(Enter your answer in INTERVAL notation, using
U
U
U
to indicate a union of intervals; or enter DNE if no solution exists)
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Background
\newline
Layout
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Theme
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Transition
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Let
x
x
x
represent any number in the set of even integers greater than
1
1
1
.
\newline
Which inequality is true for all values of
x
x
x
?
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Posted 2 months ago
Question
The Hodge conjecture is that for projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.
\newline
Hdg
(
k
)
(
X
)
=
H
(
2
k
)
(
X
,
Q
)
∩
H
(
k
,
k
)
(
X
)
\text{Hdg}^{(k)}(X) = \text{H}^{(2k)}(X,\mathbb{Q}) \cap \text{H}^{(k,k)}(X)
Hdg
(
k
)
(
X
)
=
H
(
2
k
)
(
X
,
Q
)
∩
H
(
k
,
k
)
(
X
)
.
\newline
We call this the group of Hodge classes of degree
2
k
2k
2
k
on
X
X
X
.
\newline
The modern statement of the Hodge conjecture is:
\newline
Let
X
X
X
be a non-singular complex projective manifold. Then every Hodge class on
X
X
X
is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of
X
X
X
.
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Posted 1 month ago
Question
5
5
5
b. Suppose the universal set is
ξ
=
{
0
,
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
\xi=\{0,1,2,3,4,5,6,7,8\}
ξ
=
{
0
,
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
.
\newline
i. Write in enumerated form the set that is represented by the bit string
011011001
011011001
011011001
.
\newline
ii. If
A
A
A
is represented
y
y
y
the bit string
110101110
110101110
110101110
and
B
B
B
is represented by the bit string
101011000
101011000
101011000
, write the sets AUB and A as bit strings.
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Posted 2 months ago
Question
Given:
\newline
Universal Set
U
=
2
,
4
,
5
,
6
\mathrm{U}=2,4,5,6
U
=
2
,
4
,
5
,
6
\newline
Subset B =
4
4
4
\newline
What is the complement of Set B in Set U?
\newline
{
4
}
\{4\}
{
4
}
\newline
{
2
,
4
,
5
,
6
}
\{2,4,5,6\}
{
2
,
4
,
5
,
6
}
\newline
{
2
,
5
,
6
}
\{2,5,6\}
{
2
,
5
,
6
}
\newline
{
2
,
4
,
5
}
\{2,4,5\}
{
2
,
4
,
5
}
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Posted 1 month ago
Question
Given:
\newline
Universal Set
U
=
5
,
6
,
10
,
11
,
12
\mathrm{U}=5,6,10,11,12
U
=
5
,
6
,
10
,
11
,
12
\newline
Subset B
=
10
=10
=
10
\newline
What is the complement of Set B in Set U?
\newline
{
5
,
6
,
11
,
12
}
\{5,6,11,12\}
{
5
,
6
,
11
,
12
}
\newline
{
5
,
6
,
10
,
11
}
\{5,6,10,11\}
{
5
,
6
,
10
,
11
}
\newline
{
10
}
\{10\}
{
10
}
\newline
{
5
,
6
,
10
,
11
,
12
}
\{5,6,10,11,12\}
{
5
,
6
,
10
,
11
,
12
}
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Posted 1 month ago
Question
Given:
\newline
Universal Set
U
=
4
,
5
,
6
,
7
,
11
,
12
\mathrm{U}=4,5,6,7,11,12
U
=
4
,
5
,
6
,
7
,
11
,
12
\newline
Subset B =
4
4
4
\newline
What is the complement of Set B in Set U?
\newline
{
4
,
5
,
6
,
7
,
11
,
12
}
\{4,5,6,7,11,12\}
{
4
,
5
,
6
,
7
,
11
,
12
}
\newline
{
5
,
6
,
7
,
11
,
12
}
\{5,6,7,11,12\}
{
5
,
6
,
7
,
11
,
12
}
\newline
{
4
,
5
,
6
,
11
}
\{4,5,6,11\}
{
4
,
5
,
6
,
11
}
\newline
{
4
}
\{4\}
{
4
}
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Posted 1 month ago
Question
Given:
\newline
Universal Set
U
=
4
,
5
,
7
,
8
,
10
\mathrm{U}=4,5,7,8,10
U
=
4
,
5
,
7
,
8
,
10
\newline
Subset B
=
8
=8
=
8
\newline
What is the complement of Set B in Set U?
\newline
{
4
,
5
,
7
,
8
,
10
}
\{4,5,7,8,10\}
{
4
,
5
,
7
,
8
,
10
}
\newline
{
8
}
\{8\}
{
8
}
\newline
{
4
,
5
,
8
}
\{4,5,8\}
{
4
,
5
,
8
}
\newline
{
4
,
5
,
7
,
10
}
\{4,5,7,10\}
{
4
,
5
,
7
,
10
}
Get tutor help
Posted 1 month ago