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Let’s check out your problem:
Which of the following is a solution to the inequality below?
\newline
j
≥
−
5
j \geq -5
j
≥
−
5
\newline
Choices:
\newline
(A)
j
=
−
9
j = -9
j
=
−
9
\newline
(B)
j
=
−
6
j = -6
j
=
−
6
\newline
(C)
j
=
−
12
j = -12
j
=
−
12
\newline
(D)
j
=
−
2
j = -2
j
=
−
2
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Math Problems
Grade 8
Solutions to inequalities
Full solution
Q.
Which of the following is a solution to the inequality below?
\newline
j
≥
−
5
j \geq -5
j
≥
−
5
\newline
Choices:
\newline
(A)
j
=
−
9
j = -9
j
=
−
9
\newline
(B)
j
=
−
6
j = -6
j
=
−
6
\newline
(C)
j
=
−
12
j = -12
j
=
−
12
\newline
(D)
j
=
−
2
j = -2
j
=
−
2
Evaluate Choice (A):
Evaluate choice (A)
j
=
−
9
j = -9
j
=
−
9
. Plug in the value for
j
j
j
in
j
≥
−
5
j \geq -5
j
≥
−
5
.
j
≥
−
5
j \geq -5
j
≥
−
5
Replace
j
j
j
with
−
9
-9
−
9
.
−
9
≥
−
5
-9 \geq -5
−
9
≥
−
5
Check if the inequality holds.
Check Choice (A):
Since
−
9
-9
−
9
is not greater than or equal to
−
5
-5
−
5
, choice (A) is not a solution to the inequality.
\newline
−
9
≥
−
5
-9 \geq -5
−
9
≥
−
5
is false.
Evaluate Choice (B):
Evaluate choice (B)
j
=
−
6
j = -6
j
=
−
6
.
\newline
Plug in the value for
j
j
j
in
j
≥
−
5
j \geq -5
j
≥
−
5
.
\newline
j
≥
−
5
j \geq -5
j
≥
−
5
\newline
Replace
j
j
j
with
−
6
-6
−
6
.
\newline
−
6
≥
−
5
-6 \geq -5
−
6
≥
−
5
\newline
Check if the inequality holds.
Check Choice (B):
Since
−
6
-6
−
6
is not greater than or equal to
−
5
-5
−
5
, choice (B) is not a solution to the inequality.
\newline
−
6
≥
−
5
-6 \geq -5
−
6
≥
−
5
is false.
Evaluate Choice (C):
Evaluate choice (C)
j
=
−
12
j = -12
j
=
−
12
. Plug in the value for
j
j
j
in
j
≥
−
5
j \geq -5
j
≥
−
5
.
j
≥
−
5
j \geq -5
j
≥
−
5
Replace
j
j
j
with
−
12
-12
−
12
.
−
12
≥
−
5
-12 \geq -5
−
12
≥
−
5
Check if the inequality holds.
Check Choice (C):
Since
−
12
-12
−
12
is not greater than or equal to
−
5
-5
−
5
, choice (C) is not a solution to the inequality.
\newline
−
12
≥
−
5
-12 \geq -5
−
12
≥
−
5
is false.
Evaluate Choice (D):
Evaluate choice (D)
j
=
−
2
j = -2
j
=
−
2
.
\newline
Plug in the value for
j
j
j
in
j
≥
−
5
j \geq -5
j
≥
−
5
.
\newline
j
≥
−
5
j \geq -5
j
≥
−
5
\newline
Replace
j
j
j
with
−
2
-2
−
2
.
\newline
−
2
≥
−
5
-2 \geq -5
−
2
≥
−
5
\newline
Check if the inequality holds.
Check Choice (D):
Since
−
2
-2
−
2
is greater than or equal to
−
5
-5
−
5
, choice (D) is a solution to the inequality.
\newline
−
2
≥
−
5
-2 \geq -5
−
2
≥
−
5
is true.
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