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Math Problems
Algebra 1
Solve absolute value inequalities
The perimeter of a square is increasing at a rate of
5
5
5
meters per hour.
\newline
At a certain instant, the perimeter is
30
30
30
meters.
\newline
What is the rate of change of the area of the square at that instant (in square meters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
25
16
\frac{25}{16}
16
25
\newline
(B)
5
4
\frac{5}{4}
4
5
\newline
(C)
75
4
\frac{75}{4}
4
75
\newline
(D)
25
25
25
Get tutor help
Determine the average value of the piecewise function
f
f
f
defined below on the interval
x
=
−
3
x=-3
x
=
−
3
to
x
=
6
x=6
x
=
6
. Express your answer in simplest form.
\newline
f
(
x
)
=
{
−
3
for
x
<
−
2
6
for
x
≥
−
2
f(x)=\left\{\begin{array}{lll} -3 & \text { for } & x<-2 \\ 6 & \text { for } & x \geq-2 \end{array}\right.
f
(
x
)
=
{
−
3
6
for
for
x
<
−
2
x
≥
−
2
Get tutor help
Solve for
c
c
c
.
∣
c
∣
+
2
>
16
|c| + 2 > 16
∣
c
∣
+
2
>
16
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
. Use integers, proper fractions, or improper fractions in simplest form
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
−
5
(
−
7
x
+
7
)
=
−
18
x
+
24
-5(-7 x+7)=-18 x+24
−
5
(
−
7
x
+
7
)
=
−
18
x
+
24
\newline
Get tutor help
Find the common ratio, the recursive formula, and the three terms in the sequence after the last one given.
\newline
−
2
,
6
,
−
18
,
54
,
…
r
=
\begin{array}{l} -2,6,-18,54, \ldots \\ r= \end{array}
−
2
,
6
,
−
18
,
54
,
…
r
=
\newline
a
n
=
a_{n}=
a
n
=
\newline
□
\square
□
when
a
1
=
a_{1}=
a
1
=
□
\square
□
\newline
The next three terms are
□
\square
□
,
□
\square
□
, and
□
\square
□
Get tutor help
Solve for
y
y
y
.
\newline
∣
y
∣
+
9
<
13
|y| + 9 < 13
∣
y
∣
+
9
<
13
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
r
r
r
.
\newline
8
∣
r
∣
>
16
8|r| > 16
8∣
r
∣
>
16
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
z
z
z
.
\newline
∣
−
4
z
∣
≤
4
|-4z| \leq 4
∣
−
4
z
∣
≤
4
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
w
w
w
.
\newline
∣
−
7
w
∣
≤
7
|-7w| \leq 7
∣
−
7
w
∣
≤
7
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
r
r
r
.
\newline
∣
r
∣
+
1
≤
13
|r| + 1 \leq 13
∣
r
∣
+
1
≤
13
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
p
p
p
.
\newline
∣
−
5
p
∣
≤
10
|-5p| \leq 10
∣
−
5
p
∣
≤
10
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
u
u
u
.
∣
u
−
3
∣
≥
17
|u - 3| \geq 17
∣
u
−
3∣
≥
17
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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
u
u
u
.
\newline
∣
−
4
u
∣
≥
20
|-4u| \geq 20
∣
−
4
u
∣
≥
20
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
\newline
Get tutor help
Solve for
s
s
s
.
\newline
∣
s
∣
−
3
≤
11
|s| - 3 \leq 11
∣
s
∣
−
3
≤
11
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
q
q
q
.
\newline
−
6
∣
q
∣
≤
−
12
-6|q| \leq -12
−
6∣
q
∣
≤
−
12
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
t
t
t
.
\newline
∣
−
9
t
∣
<
18
|-9t| < 18
∣
−
9
t
∣
<
18
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
d
d
d
.
∣
d
∣
−
1
<
17
|d| - 1 < 17
∣
d
∣
−
1
<
17
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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
t
t
t
.
\newline
−
9
∣
t
∣
>
−
18
-9|t| > -18
−
9∣
t
∣
>
−
18
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
d
d
d
.
\newline
−
∣
d
∣
<
−
20
-|d| < -20
−
∣
d
∣
<
−
20
\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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
s
s
s
.
\newline
−
3
∣
s
∣
≥
−
15
-3|s| \geq -15
−
3∣
s
∣
≥
−
15
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
z
z
z
.
∣
z
∣
−
8
≤
9
|z| - 8 \leq 9
∣
z
∣
−
8
≤
9
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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
u
u
u
.
\newline
∣
−
u
∣
>
14
|-u| > 14
∣
−
u
∣
>
14
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
w
w
w
.
\newline
∣
5
w
∣
>
5
|5w| > 5
∣5
w
∣
>
5
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
r
r
r
.
\newline
7
∣
r
∣
≥
7
7|r| \geq 7
7∣
r
∣
≥
7
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
v
v
v
.
∣
−
4
v
∣
≤
4
|{-4v}| \leq 4
∣
−
4
v
∣
≤
4
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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
b
b
b
.
\newline
6
∣
b
∣
≤
6
6|b| \leq 6
6∣
b
∣
≤
6
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
_
_
\_\_
__
Get tutor help
Solve for
b
b
b
.
\newline
∣
b
∣
−
7
>
−
5
|b| - 7 > -5
∣
b
∣
−
7
>
−
5
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
z
z
z
.
\newline
∣
−
2
z
∣
≤
18
|-2z| \leq 18
∣
−
2
z
∣
≤
18
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
b
b
b
.
∣
b
∣
−
7
≤
7
|b| - 7 \leq 7
∣
b
∣
−
7
≤
7
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
. Use integers, proper fractions, or improper fractions in simplest form.______
Get tutor help
Solve for
r
r
r
.
∣
r
−
8
∣
≥
8
|r - 8| \geq 8
∣
r
−
8∣
≥
8
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
. Use integers, proper fractions, or improper fractions in simplest form.______
Get tutor help
Solve for
w
w
w
.
\newline
∣
2
w
∣
<
10
|2w| < 10
∣2
w
∣
<
10
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
s
s
s
.
\newline
∣
s
∣
+
2
≥
18
|s| + 2 \geq 18
∣
s
∣
+
2
≥
18
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
w
w
w
.
\newline
∣
w
+
8
∣
<
9
|w + 8| < 9
∣
w
+
8∣
<
9
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
y
y
y
.
∣
y
−
3
∣
≥
12
|y - 3| \geq 12
∣
y
−
3∣
≥
12
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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
d
d
d
.
∣
d
∣
+
5
>
15
|d| + 5 > 15
∣
d
∣
+
5
>
15
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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
w
w
w
.
\newline
∣
−
2
w
∣
>
14
|-2w| > 14
∣
−
2
w
∣
>
14
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
w
w
w
.
\newline
−
2
∣
w
∣
≤
−
12
-2|w| \leq -12
−
2∣
w
∣
≤
−
12
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
d
d
d
.
\newline
−
7
∣
d
∣
>
−
14
-7|d| > -14
−
7∣
d
∣
>
−
14
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
s
s
s
.
\newline
∣
s
−
6
∣
>
8
|s - 6| > 8
∣
s
−
6∣
>
8
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
w
w
w
.
\newline
∣
w
∣
+
7
>
17
|w| + 7 > 17
∣
w
∣
+
7
>
17
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Solve for
w
w
w
.
\newline
∣
−
w
∣
≤
12
|-w| \leq 12
∣
−
w
∣
≤
12
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Solve for
y
y
y
.
\newline
−
7
∣
y
∣
≥
−
14
-7|y| \geq -14
−
7∣
y
∣
≥
−
14
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Solve for
w
w
w
.
\newline
∣
w
∣
−
9
≥
−
4
|w| - 9 \geq -4
∣
w
∣
−
9
≥
−
4
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Solve for
z
z
z
.
∣
z
∣
−
2
≤
5
|z| - 2 \leq 5
∣
z
∣
−
2
≤
5
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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
t
t
t
.
\newline
−
∣
t
∣
<
−
8
-|t| < -8
−
∣
t
∣
<
−
8
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Solve for
v
v
v
.
\newline
∣
v
∣
−
7
>
−
2
\lvert v \rvert - 7 > -2
∣
v
∣
−
7
>
−
2
\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
. Use integers, proper fractions, or improper fractions in simplest form.
Get tutor help
Solve for
v
v
v
.
\newline
−
5
∣
v
∣
>
−
10
-5|v| > -10
−
5∣
v
∣
>
−
10
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
p
p
p
.
\newline
∣
p
+
1
∣
<
9
|p + 1| < 9
∣
p
+
1∣
<
9
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
Get tutor help
Solve for
t
t
t
.
\newline
∣
t
+
8
∣
≤
4
|t + 8| \leq 4
∣
t
+
8∣
≤
4
\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
. Use integers, proper fractions, or improper fractions in simplest form.
\newline
______
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Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
g
(
f
(
2
)
)
g(f(2))
g
(
f
(
2
))
.
\newline
f
(
x
)
=
−
5
x
+
3
g
(
x
)
=
2
x
2
+
5
x
−
14
\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}
f
(
x
)
=
−
5
x
+
3
g
(
x
)
=
2
x
2
+
5
x
−
14
\newline
Answer:
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