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Math Problems
Grade 6
Integer inequalities with absolute values
If
r
r
r
is an integer, which of the following is a solution for
4
+
∣
2
r
−
3
∣
=
11
4+|2 r-3|=11
4
+
∣2
r
−
3∣
=
11
? Select all that apply.
\newline
−
9
-9
−
9
\newline
−
6
-6
−
6
\newline
−
5
-5
−
5
\newline
−
2
-2
−
2
\newline
2
2
2
\newline
5
5
5
\newline
6
6
6
\newline
9
9
9
Get tutor help
Find the value of the given expression if
x
=
1
x=1
x
=
1
and
y
=
−
5
y=-5
y
=
−
5
.
\newline
∣
7
x
−
3
y
∣
|7 x-3 y|
∣7
x
−
3
y
∣
\newline
∣
7
x
−
3
y
∣
=
26
|7 x-3 y|=26
∣7
x
−
3
y
∣
=
26
(Simplify your answer.)
Get tutor help
Which sign makes the statement true?
\newline
∣
5
∣
\lvert 5 \rvert
∣
5
∣
?
9
9
9
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
5
?
∣
−
5
∣
5 \,?\, \lvert -5 \rvert
5
?
∣
−
5
∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
1
?
∣
−
7
∣
1 ? |-7|
1
?
∣
−
7∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
6
?
∣
−
1
∣
-6 \, ? \, |\,-1|
−
6
?
∣
−
1∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
2
∣
\lvert 2 \rvert
∣
2
∣
?
−
8
-8
−
8
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
9
∣
\lvert -9 \rvert
∣
−
9
∣
?
−
8
-8
−
8
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
2
∣
\lvert -2 \rvert
∣
−
2
∣
?
0
0
0
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
8
?
∣
−
6
∣
-8 \, ? \, |\,-6|
−
8
?
∣
−
6∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
7
?
∣
−
1
∣
7 \,?\, |\,-1\,|
7
?
∣
−
1
∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
9
∣
\lvert -9 \rvert
∣
−
9
∣
?
4
4
4
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
0
?
∣
0
∣
0 \,?\, |0|
0
?
∣0∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
5
∣
\lvert 5 \rvert
∣
5
∣
?
−
6
-6
−
6
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
5
∣
\lvert -5 \rvert
∣
−
5
∣
?
4
4
4
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
9
∣
\lvert -9 \rvert
∣
−
9
∣
?
−
9
-9
−
9
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
2
?
∣
6
∣
2 \, ? \, |6|
2
?
∣6∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
9
∣
\lvert -9 \rvert
∣
−
9
∣
?
−
3
-3
−
3
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
6
∣
\lvert -6 \rvert
∣
−
6
∣
?
4
4
4
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
3
∣
?
4
|-3| \, ? \, 4
∣
−
3∣
?
4
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
5
?
∣
−
1
∣
5 \,?\, \lvert -1 \rvert
5
?
∣
−
1
∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
1
?
∣
−
4
∣
-1 \, ? \, \lvert -4 \rvert
−
1
?
∣
−
4
∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Solve the absolute value equation. Check your solutions.
\newline
∣
x
+
4
∣
=
10
|x+4|=10
∣
x
+
4∣
=
10
Get tutor help
Which sign makes the statement true?
\newline
∣
−
3
∣
\lvert -3 \rvert
∣
−
3
∣
?
−
7
-7
−
7
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
2
∣
\lvert -2 \rvert
∣
−
2
∣
?
−
1
-1
−
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
3
∣
\lvert -3 \rvert
∣
−
3
∣
?
−
8
-8
−
8
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
4
∣
\lvert 4 \rvert
∣
4
∣
?
3
3
3
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
9
-9
−
9
?
∣
4
∣
|4|
∣4∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
2
-2
−
2
?
∣
−
2
∣
|-2|
∣
−
2∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
7
-7
−
7
?
∣
8
∣
|8|
∣8∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
7
-7
−
7
?
∣
7
∣
|7|
∣7∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
4
∣
\lvert 4 \rvert
∣
4
∣
?
−
5
-5
−
5
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
2
?
∣
−
7
∣
2 \,?\, \lvert -7 \rvert
2
?
∣
−
7
∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
4
?
∣
−
1
∣
-4 \, ? \, |\,-1|
−
4
?
∣
−
1∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
9
∣
\lvert 9 \rvert
∣
9
∣
?
−
2
-2
−
2
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
3
?
∣
−
7
∣
-3 \, ? \, |\,-7|
−
3
?
∣
−
7∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
0
?
∣
-
8
∣
0 \ ? \ |\text{-}8|
0
?
∣
-
8∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
9
∣
\lvert -9 \rvert
∣
−
9
∣
?
−
6
-6
−
6
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
0
∣
\lvert 0 \rvert
∣
0
∣
?
0
0
0
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
7
∣
\lvert 7 \rvert
∣
7
∣
?
1
1
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
3
?
∣
3
∣
3 \, ? \, |3|
3
?
∣3∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
−
4
?
∣
−
8
∣
-4 \, ? \, |\,-8|
−
4
?
∣
−
8∣
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Which sign makes the statement true?
\newline
∣
−
7
∣
\lvert -7 \rvert
∣
−
7
∣
?
1
1
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Solve the absolute value equation. Check your solutions.
\newline
∣
x
+
8
∣
=
12
|x+8|=12
∣
x
+
8∣
=
12
Get tutor help
|
3
3
3
x+
4
4
4
|=
16
16
16
\newline
◻
\newline
Get tutor help
Solve for
y
y
y
:
\newline
∣
4
y
−
2
∣
+
7
=
37
|4 y-2|+7=37
∣4
y
−
2∣
+
7
=
37
Get tutor help
Solve for all values of
x
x
x
in simplest form.
\newline
8
+
5
∣
3
x
−
3
∣
=
18
8+5|3 x-3|=18
8
+
5∣3
x
−
3∣
=
18
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve
5
∣
x
+
3
∣
−
12
≤
13
5|x+3|-12 \leq 13
5∣
x
+
3∣
−
12
≤
13
.
\newline
(A) There are no solutions.
\newline
(B)
−
2
≤
x
≤
2
-2 \leq x \leq 2
−
2
≤
x
≤
2
\newline
(C)
−
8
≤
x
≤
8
-8 \leq x \leq 8
−
8
≤
x
≤
8
\newline
(D)
−
8
≤
x
≤
2
-8 \leq x \leq 2
−
8
≤
x
≤
2
Get tutor help
Which sign makes the statement true?
\newline
−
7
?
∣
−
7
∣
-7 \text { ? }|-7|
−
7
?
∣
−
7∣
\newline
<
\newline
>
\newline
=
Get tutor help
−
2
∣
2
x
+
12
∣
−
1
=
−
17
-2|2 x+12|-1=-17
−
2∣2
x
+
12∣
−
1
=
−
17
Get tutor help
1
2
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