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Math Problems
Algebra 1
Solve advanced linear inequalities
Solve for
x
x
x
.
\newline
−
18
x
+
21
>
−
15
OR
20
x
−
13
≥
27
-18 x+21>-15 \quad \text { OR } \quad 20 x-13 \geq 27
−
18
x
+
21
>
−
15
OR
20
x
−
13
≥
27
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2
=
−
5
(
b
+
8
)
−
13
b
=
□
\begin{array}{l}2=-5(b+8)-13 \\ b=\square\end{array}
2
=
−
5
(
b
+
8
)
−
13
b
=
□
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Solve for
x
x
x
.
\newline
3
x
−
91
>
−
87
AND
17
x
−
16
>
18
3 x-91>-87 \quad \text { AND } \quad 17 x-16>18
3
x
−
91
>
−
87
AND
17
x
−
16
>
18
\newline
Choose
1
1
1
answer:
\newline
(A)
x
>
2
x>2
x
>
2
\newline
(B)
x
>
4
3
x>\frac{4}{3}
x
>
3
4
\newline
(c)
4
3
<
x
<
2
\frac{4}{3}<x<2
3
4
<
x
<
2
\newline
(D) There are no solutions
\newline
(E) All values of
x
x
x
are solutions
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Select the expressions that are equivalent to
2
(
m
+
7
)
2(m + 7)
2
(
m
+
7
)
.
\newline
Multi-select Choices:
\newline
(A)
9
m
9m
9
m
\newline
(B)
7
(
m
+
2
)
7(m + 2)
7
(
m
+
2
)
\newline
(C)
(
m
×
7
)
2
(m \times 7)2
(
m
×
7
)
2
\newline
(D)
2
m
+
14
2m + 14
2
m
+
14
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x
2
−
36
>
0
x^2-36>0
x
2
−
36
>
0
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Solve for
x
x
x
.
\newline
3
x
+
10
=
25
3x+10 = 25
3
x
+
10
=
25
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Integrate
ln
[
(
x
)
(
1
−
x
)
]
\ln[(x)(1-x)]
ln
[(
x
)
(
1
−
x
)]
in the limits
0
0
0
to
1
1
1
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Solve for
b
b
b
.
\newline
b
+
18
16
>
1
b + \frac{18}{16} > 1
b
+
16
18
>
1
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Solve for
a
a
a
.
\newline
a
−
1
5
>
1
a - \frac{1}{5} > 1
a
−
5
1
>
1
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Solve for
r
r
r
.
3
(
r
+
7
)
+
7
<
1
3(r + 7) + 7 < 1
3
(
r
+
7
)
+
7
<
1
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Solve for
b
b
b
.
\newline
3
(
b
−
17
)
+
14
>
8
3(b - 17) + 14 > 8
3
(
b
−
17
)
+
14
>
8
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Solve for
d
d
d
.
\newline
2
(
d
−
16
)
−
6
≥
2
2(d - 16) - 6 \geq 2
2
(
d
−
16
)
−
6
≥
2
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Solve for
y
y
y
.
\newline
4
(
y
+
2
)
≥
12
4(y + 2) \geq 12
4
(
y
+
2
)
≥
12
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Solve for
s
s
s
.
\newline
7
(
s
−
19
)
+
19
≥
5
7(s - 19) + 19 \geq 5
7
(
s
−
19
)
+
19
≥
5
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x
2
(
x
−
2
)
(
x
+
3
)
2
<
0
x^2(x-2)(x+3)^2<0
x
2
(
x
−
2
)
(
x
+
3
)
2
<
0
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Solve the inequality,
4
−
3
(
2
−
x
)
<
10
+
x
4-3(2-x)<10+x
4
−
3
(
2
−
x
)
<
10
+
x
.
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Solve for
z
\mathrm{z}
z
.
\newline
5
z
+
8
=
3
z
+
16
5z+8=3z+16
5
z
+
8
=
3
z
+
16
\newline
z
=
□
z = \square
z
=
□
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56
<
8
(
x
+
4
)
<
120
56<8(x+4)<120
56
<
8
(
x
+
4
)
<
120
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x
−
2
x
+
3
>
−
2
\frac{x-2}{x+3}>-2
x
+
3
x
−
2
>
−
2
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Prove that
1
2
−
1
+
2
3
+
1
⇒
2
+
3
\frac{1}{\sqrt{2}-1}+\frac{2}{\sqrt{3}+1} \Rightarrow \sqrt{2}+\sqrt{3}
2
−
1
1
+
3
+
1
2
⇒
2
+
3
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x
2
−
5
≤
3
(
x
+
2
)
<
9
\frac{x}{2}-5 \leq 3(x+2)<9
2
x
−
5
≤
3
(
x
+
2
)
<
9
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2
p
+
5
>
2
(
p
−
3
)
2 p+5>2(p-3)
2
p
+
5
>
2
(
p
−
3
)
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1
<
e
x
−
1
ln
(
x
−
1
)
<
(
x
+
1
)
=
x
1<\frac{e^{x}-1}{\ln (x-1)}<(x+1)=x
1
<
l
n
(
x
−
1
)
e
x
−
1
<
(
x
+
1
)
=
x
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Exercise: G.M.V.T.
\newline
1
<
e
x
−
1
ln
(
x
+
1
)
<
(
x
+
1
)
e
x
1<\frac{e^{x}-1}{\ln (x+1)}<(x+1) e^{x}
1
<
ln
(
x
+
1
)
e
x
−
1
<
(
x
+
1
)
e
x
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Exercise: G.M.L.T.
\newline
1
<
e
x
−
1
ln
(
x
+
1
)
<
(
x
+
1
)
e
x
1<\frac{e^{x}-1}{\ln (x+1)}<(x+1) e^{x}
1
<
ln
(
x
+
1
)
e
x
−
1
<
(
x
+
1
)
e
x
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15
15
15
−
6
-6
−
6
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15
−
6
15-6
15
−
6
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What is the sum of the solutions to the equation
(
t
+
3
)
(
t
−
357
)
=
0
(t+3)(t-357)=0
(
t
+
3
)
(
t
−
357
)
=
0
?
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Solve for
q
q
q
.
\newline
1
<
q
−
15
−
18
1 < \frac{q - 15}{-18}
1
<
−
18
q
−
15
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Solve for
c
c
c
.
\newline
−
16
<
c
−
14
<
1
-16 < c - 14 < 1
−
16
<
c
−
14
<
1
\newline
Express your answer as a compound inequality with integers.
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Solve for
p
p
p
.
\newline
0
<
p
+
16
<
13
0 < p + 16 < 13
0
<
p
+
16
<
13
\newline
Express your answer as a compound inequality with integers.
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Solve for
n
n
n
.
\newline
n
−
14
−
1
≤
20
\frac{n - 14}{-1} \leq 20
−
1
n
−
14
≤
20
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Solve for
u
u
u
.
\newline
−
14
≤
2
(
u
+
5
)
−
10
-14 \leq 2(u + 5) - 10
−
14
≤
2
(
u
+
5
)
−
10
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Solve for
n
n
n
.
10
≤
2
(
n
+
11
)
10 \leq 2(n + 11)
10
≤
2
(
n
+
11
)
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Solve for
d
d
d
.
\newline
10
≤
5
(
d
−
17
)
10 \leq 5(d - 17)
10
≤
5
(
d
−
17
)
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Solve for
y
y
y
.
\newline
−
2
(
y
−
11
)
≤
2
-2(y - 11) \leq 2
−
2
(
y
−
11
)
≤
2
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Solve for
h
h
h
.
\newline
−
5
≥
5
(
h
−
10
)
-5 \geq 5(h - 10)
−
5
≥
5
(
h
−
10
)
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Solve for
k
k
k
.
4
<
k
−
9
−
3
4 < \frac{k - 9}{-3}
4
<
−
3
k
−
9
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Solve for
q
q
q
.
\newline
−
2
(
q
+
10
)
−
15
>
−
11
-2(q + 10) - 15 > -11
−
2
(
q
+
10
)
−
15
>
−
11
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Solve for
u
u
u
.
\newline
3
(
u
+
1
)
≥
12
3(u + 1) \geq 12
3
(
u
+
1
)
≥
12
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Solve for
k
k
k
.
\newline
−
13
≥
3
(
k
+
3
)
−
7
-13 \geq 3(k + 3) - 7
−
13
≥
3
(
k
+
3
)
−
7
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Solve for
y
y
y
.
\newline
−
11
<
20
(
y
−
4
)
+
9
-11 < 20(y - 4) + 9
−
11
<
20
(
y
−
4
)
+
9
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Solve for
p
p
p
.
p
−
6
−
2
≤
−
1
\frac{p - 6}{-2} \leq -1
−
2
p
−
6
≤
−
1
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Solve for
g
g
g
.
2
(
g
−
6
)
≤
12
2(g - 6) \leq 12
2
(
g
−
6
)
≤
12
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Solve for
z
z
z
.
\newline
−
2
≤
z
−
2
2
-2 \leq \frac{z - 2}{2}
−
2
≤
2
z
−
2
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Solve for
s
s
s
.
\newline
−
1
(
s
−
6
)
≥
3
-1(s - 6) \geq 3
−
1
(
s
−
6
)
≥
3
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Solve for
m
m
m
.
\newline
−
6
(
m
+
16
)
−
13
>
5
-6(m + 16) - 13 > 5
−
6
(
m
+
16
)
−
13
>
5
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Solve for
k
k
k
.
\newline
2
(
k
+
7
)
+
10
≥
18
2(k + 7) + 10 \geq 18
2
(
k
+
7
)
+
10
≥
18
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Solve for
b
b
b
.
\newline
18
>
−
6
(
b
+
7
)
+
12
18 > -6(b + 7) + 12
18
>
−
6
(
b
+
7
)
+
12
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Solve for
f
f
f
.
2
(
f
−
16
)
+
7
≤
11
2(f - 16) + 7 \leq 11
2
(
f
−
16
)
+
7
≤
11
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1
2
3
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