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Math Problems
Algebra 2
Solve quadratic inequalities
Solve for
x
x
x
.
\newline
(
x
−
1
)
(
x
+
1
)
>
0
(x - 1)(x + 1) > 0
(
x
−
1
)
(
x
+
1
)
>
0
\newline
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
\newline
______
\newline
Get tutor help
x
−
6
y
>
5
7
x
+
2
y
≥
4
\begin{array}{l} x-6 y>5 \\ 7 x+2 y \geq 4 \end{array}
x
−
6
y
>
5
7
x
+
2
y
≥
4
\newline
Is
(
10
,
−
2
)
(10,-2)
(
10
,
−
2
)
a solution of the system?
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7
x
−
9
y
<
5
−
2
x
+
4
y
>
5
\begin{array}{l} 7 x-9 y<5 \\ -2 x+4 y>5 \end{array}
7
x
−
9
y
<
5
−
2
x
+
4
y
>
5
\newline
Is
(
3
,
5
)
(3,5)
(
3
,
5
)
a solution of the system?
Get tutor help
Solve the inequality for
x
x
x
.
\newline
−
1
+
x
4
<
4
-1+\frac{x}{4}<4
−
1
+
4
x
<
4
\newline
Simplify your answer as much as possible.
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2
2
2
.
(
x
+
3
)
3
(
x
−
1
)
2
(
x
−
4
)
≥
0
(x+3)^{3}(x-1)^{2}(x-4) \geq 0
(
x
+
3
)
3
(
x
−
1
)
2
(
x
−
4
)
≥
0
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y
=
−
x
(
x
+
6
)
+
18
y=-x(x+6)+18
y
=
−
x
(
x
+
6
)
+
18
\newline
y
=
−
7
x
+
12
y=-7x+12
y
=
−
7
x
+
12
\newline
if
a
,
b
a,b
a
,
b
is a solution to the system of equations shown and
b
<
0
b<0
b
<
0
what is the value of
a
a
a
Get tutor help
3
3
3
What value of
x
x
x
makes the equation
(
x
−
6
)
−
8
x
=
−
2
+
5
(
2
+
1
)
(x-6)-8 x=-2+5(2+1)
(
x
−
6
)
−
8
x
=
−
2
+
5
(
2
+
1
)
Get tutor help
Khan Academfet AI Tutoring
\newline
NEW
\newline
Find the inequality represented by the graph.
\newline
x
<
−
3
2
x
−
2
x<-\frac{3}{2} x-2
x
<
−
2
3
x
−
2
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
8
?
−
8
-8 \,?\, -8
−
8
?
−
8
\newline
You can use the number line to help.
\newline
Choices:
\newline
(
A
)
>
(A) >
(
A
)
>
\newline
(
B
)
<
(B) <
(
B
)
<
\newline
(
C
)
=
(C) =
(
C
)
=
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
5
?
5
-5 \,?\, 5
−
5
?
5
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
4
?
0
-4 \, ? \, 0
−
4
?
0
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
3
?
7
-3 \, ? \, 7
−
3
?
7
\newline
You can use the number line to help.
\newline
Choices:
\newline
(
A
)
>
(A) >
(
A
)
>
\newline
(
B
)
<
(B) <
(
B
)
<
\newline
(
C
)
=
(C) =
(
C
)
=
Get tutor help
1
1
1
.
(
x
−
12
)
+
y
+
z
?
(x-12)+y+z ?
(
x
−
12
)
+
y
+
z
?
for
x
=
−
23
,
y
=
−
5
x=-23, y=-5
x
=
−
23
,
y
=
−
5
, and
z
=
−
10
z=-10
z
=
−
10
Get tutor help
Solve for
w
w
w
.
\newline
−
2
w
=
−
6
-\frac{2}{w}=-6
−
w
2
=
−
6
\newline
Simplify your answer as much as possible.
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z
3
≤
3
\frac{z}{3} \leq 3
3
z
≤
3
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Graph the inequality on the axes below.
\newline
y
≥
−
5
4
x
−
5
y \geq-\frac{5}{4} x-5
y
≥
−
4
5
x
−
5
Get tutor help
Find
lim
h
→
0
6
arctan
(
1
+
h
)
−
6
arctan
(
1
)
h
\lim _{h \rightarrow 0} \frac{6 \arctan (1+h)-6 \arctan (1)}{h}
lim
h
→
0
h
6
a
r
c
t
a
n
(
1
+
h
)
−
6
a
r
c
t
a
n
(
1
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
3
3
3
\newline
(C)
6
6
6
\newline
(D) The limit doesn't exist
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Find
lim
h
→
0
6
9
+
h
−
6
9
h
\lim _{h \rightarrow 0} \frac{6 \sqrt{9+h}-6 \sqrt{9}}{h}
lim
h
→
0
h
6
9
+
h
−
6
9
.
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
6
6
6
\newline
(C)
18
18
18
\newline
(D) The limit doesn't exist
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Find
lim
h
→
0
4
sin
(
π
2
+
h
)
−
4
sin
(
π
2
)
h
\lim _{h \rightarrow 0} \frac{4 \sin \left(\frac{\pi}{2}+h\right)-4 \sin \left(\frac{\pi}{2}\right)}{h}
lim
h
→
0
h
4
s
i
n
(
2
π
+
h
)
−
4
s
i
n
(
2
π
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
1
1
1
\newline
(C)
4
4
4
\newline
(D) The limit doesn't exist
Get tutor help
What is the value of
n
n
n
in the equation
5
n
+
3
(
n
−
4
)
=
36
5n+3(n-4)=36
5
n
+
3
(
n
−
4
)
=
36
?
Get tutor help
let
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
and
g
(
x
)
=
x
x
g(x)=\frac{x}{x}
g
(
x
)
=
x
x
explain, why
lim
x
→
2
(
f
(
x
)
)
=
0
\lim_{x\to 2}(f(x))=0
lim
x
→
2
(
f
(
x
))
=
0
,
lim
x
→
0
(
g
(
x
)
)
=
0
\lim_{x\to 0}(g(x))=0
lim
x
→
0
(
g
(
x
))
=
0
and why
lim
x
→
2
(
g
(
f
(
x
)
)
\lim_{x\to 2}(g(f(x))
lim
x
→
2
(
g
(
f
(
x
))
does not exist
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S
15
S_{15}
S
15
if
a
1
a_{1}
a
1
and
a
n
=
−
2
a
a_{n}=-2 a
a
n
=
−
2
a
Get tutor help
x
−
1
x
+
1
−
x
+
1
x
−
1
<
2
\frac{x-1}{x+1}-\frac{x+1}{x-1}<2
x
+
1
x
−
1
−
x
−
1
x
+
1
<
2
Get tutor help
g
(
x
)
=
x
−
1
3
g(x)= \sqrt[3]{x-1}
g
(
x
)
=
3
x
−
1
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
5
)
(
x
−
6
)
≥
0
(x - 5)(x - 6) \geq 0
(
x
−
5
)
(
x
−
6
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
1
)
(
x
−
2
)
≤
0
(x - 1)(x - 2) \leq 0
(
x
−
1
)
(
x
−
2
)
≤
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
+
2
)
≥
0
x(x + 2) \geq 0
x
(
x
+
2
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
+
4
)
>
0
x(x + 4) > 0
x
(
x
+
4
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
−
5
)
>
0
x(x - 5) > 0
x
(
x
−
5
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
2
)
(
x
+
3
)
≥
0
(x - 2)(x + 3) \geq 0
(
x
−
2
)
(
x
+
3
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
4
)
(
x
+
6
)
<
0
(x - 4)(x + 6) < 0
(
x
−
4
)
(
x
+
6
)
<
0
\newline
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
+
1
)
(
x
−
2
)
≥
0
(x + 1)(x - 2) \geq 0
(
x
+
1
)
(
x
−
2
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
+
2
)
(
x
−
6
)
<
0
(x + 2)(x - 6) < 0
(
x
+
2
)
(
x
−
6
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
1
)
(
x
+
5
)
<
0
(x - 1)(x + 5) < 0
(
x
−
1
)
(
x
+
5
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
+
1
)
(
x
−
4
)
>
0
(x + 1)(x - 4) > 0
(
x
+
1
)
(
x
−
4
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
3
)
(
x
−
6
)
>
0
(x - 3)(x - 6) > 0
(
x
−
3
)
(
x
−
6
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
5
)
(
x
−
6
)
>
0
(x - 5)(x - 6) > 0
(
x
−
5
)
(
x
−
6
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
2
)
(
x
−
3
)
>
0
(x - 2)(x - 3) > 0
(
x
−
2
)
(
x
−
3
)
>
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
1
)
(
x
−
2
)
<
0
(x - 1)(x - 2) < 0
(
x
−
1
)
(
x
−
2
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
(
x
+
2
)
(
x
+
3
)
≥
0
(x + 2)(x + 3) \geq 0
(
x
+
2
)
(
x
+
3
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
4
)
(
x
+
5
)
<
0
(x - 4)(x + 5) < 0
(
x
−
4
)
(
x
+
5
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
+
4
)
(
x
−
4
)
<
0
(x + 4)(x - 4) < 0
(
x
+
4
)
(
x
−
4
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
−
2
)
≥
0
x(x - 2) \geq 0
x
(
x
−
2
)
≥
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
3
)
(
x
−
6
)
<
0
(x - 3)(x - 6) < 0
(
x
−
3
)
(
x
−
6
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
+
2
)
≤
0
x(x + 2) \leq 0
x
(
x
+
2
)
≤
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
+
6
)
<
0
x(x + 6) < 0
x
(
x
+
6
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
6
)
(
x
+
6
)
<
0
(x - 6)(x + 6) < 0
(
x
−
6
)
(
x
+
6
)
<
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
1
)
(
x
+
6
)
≤
0
(x - 1)(x + 6) \leq 0
(
x
−
1
)
(
x
+
6
)
≤
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
Get tutor help
Solve for
x
x
x
.
\newline
(
x
−
2
)
(
x
−
3
)
≤
0
(x - 2)(x - 3) \leq 0
(
x
−
2
)
(
x
−
3
)
≤
0
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.______
Get tutor help
Solve for
x
x
x
.
\newline
x
(
x
−
4
)
<
0
x(x - 4) < 0
x
(
x
−
4
)
<
0
\newline
\newline
Write a compound inequality like
1
<
x
<
3
1 < x < 3
1
<
x
<
3
or like
x
<
1
x < 1
x
<
1
or
x
>
3
x > 3
x
>
3
.
\newline
______
\newline
Get tutor help
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