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Math Problems
Algebra 1
Create linear equations with no solutions or infinitely many solutions
Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer.
\newline
−
2
x
+
4
+
3
x
=
x
−
4
-2 x+4+3 x=x-4
−
2
x
+
4
+
3
x
=
x
−
4
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Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer.
\newline
10
x
−
5
=
−
5
x
−
5
+
15
x
10 x-5=-5 x-5+15 x
10
x
−
5
=
−
5
x
−
5
+
15
x
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Find the missing number so that the equation has infinitely many solutions.
\newline
5
x
+
_
_
_
_
=
5
x
+
13
5x + \_\_\_\_ = 5x + 13
5
x
+
____
=
5
x
+
13
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Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
+
4
=
3
x
+
8
\_\_\_\_x + 4 = 3x + 8
____
x
+
4
=
3
x
+
8
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Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
+
2
=
−
3
x
−
11
\_\_\_\_x + 2 = -3x - 11
____
x
+
2
=
−
3
x
−
11
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Find the missing number so that the equation has infinitely many solutions.
\newline
−
5
x
+
11
=
_
_
_
_
x
+
11
-5x + 11 = \_\_\_\_x + 11
−
5
x
+
11
=
____
x
+
11
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Find the missing number so that the equation has infinitely many solutions.
\newline
2
x
+
8
=
2
x
+
‾
2x + 8 = 2x + \underline{\hspace{1cm}}
2
x
+
8
=
2
x
+
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Find the missing number so that the equation has infinitely many solutions.
\newline
2
x
−
2
=
2
x
+
‾
2x - 2 = 2x + \underline{\hspace{1cm}}
2
x
−
2
=
2
x
+
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Find the missing number so that the equation has infinitely many solutions.
\newline
_
_
_
_
x
−
2
=
−
4
x
−
2
\_\_\_\_x - 2 = -4x - 2
____
x
−
2
=
−
4
x
−
2
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Find the missing number so that the equation has infinitely many solutions.
\newline
3
x
+
_
_
_
_
=
3
x
+
3
3x + \_\_\_\_ = 3x + 3
3
x
+
____
=
3
x
+
3
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Find the missing number so that the equation has no solutions.
\newline
2
x
−
5
=
_
_
_
_
x
−
18
2x - 5 = \_\_\_\_x - 18
2
x
−
5
=
____
x
−
18
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Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
−
16
=
−
2
x
+
5
\_\_\_\_x - 16 = -2x + 5
____
x
−
16
=
−
2
x
+
5
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Find the missing number so that the equation has no solutions.
\newline
−
3
x
−
17
=
_
_
_
_
x
+
17
-3x - 17 = \_\_\_\_x + 17
−
3
x
−
17
=
____
x
+
17
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Find the missing number so that the equation has no solutions.
\newline
3
x
+
16
=
_
_
_
_
x
−
3
3x + 16 = \_\_\_\_x - 3
3
x
+
16
=
____
x
−
3
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Find the missing number so that the equation has infinitely many solutions.
\newline
4
x
−
6
=
‾
x
−
6
4x - 6 = \underline{\hspace{1cm}}x - 6
4
x
−
6
=
x
−
6
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Find the missing number so that the equation has infinitely many solutions.
\newline
−
2
x
+
2
=
‾
x
+
2
-2x + 2 = \underline{\hspace{1cm}}x + 2
−
2
x
+
2
=
x
+
2
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Find the missing number so that the equation has no solutions.
\newline
−
5
x
−
18
=
_
_
_
_
x
−
12
-5x - 18 = \_\_\_\_x - 12
−
5
x
−
18
=
____
x
−
12
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Find the missing number so that the equation has infinitely many solutions.
\newline
2
x
−
18
=
‾
x
−
18
2x - 18 = \underline{\hspace{1cm}}x - 18
2
x
−
18
=
x
−
18
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Find the missing number so that the equation has infinitely many solutions.
\newline
5
x
−
13
=
5
x
+
‾
5x - 13 = 5x + \underline{\hspace{1cm}}
5
x
−
13
=
5
x
+
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
4
x
−
15
=
‾
x
−
15
4x - 15 = \underline{\hspace{1cm}}x - 15
4
x
−
15
=
x
−
15
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Find the missing number so that the equation has infinitely many solutions.
\newline
−
3
x
+
‾
=
−
3
x
+
5
-3x + \underline{\hspace{1cm}} = -3x + 5
−
3
x
+
=
−
3
x
+
5
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Extraneous solutions of equations
\newline
Rania solves the equation below by first squaring both sides of the equation.
\newline
−
5
=
3
x
−
7
-5=\sqrt{3 x-7}
−
5
=
3
x
−
7
\newline
What extraneous solution does Rania obtain?
\newline
x
=
x=
x
=
\newline
□
\square
□
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What value of
x
x
x
makes this equation
\newline
true?
\newline
−
38
=
x
−
42
-38=x-42
−
38
=
x
−
42
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Simplify. Write your answer using whole numbers and variables.
\newline
8
2
z
+
2
\frac{8}{2z + 2}
2
z
+
2
8
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Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
+
14
=
−
4
x
−
8
\_\_\_\_x + 14 = -4x - 8
____
x
+
14
=
−
4
x
−
8
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
4
x
+
_
_
_
_
=
4
x
+
2
4x + \_\_\_\_ = 4x + 2
4
x
+
____
=
4
x
+
2
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Find the missing number so that the equation has infinitely many solutions.
\newline
4
x
+
_
_
_
_
=
4
x
+
17
4x + \_\_\_\_ = 4x + 17
4
x
+
____
=
4
x
+
17
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y
=
−
2
x
−
5
y=-2x-5
y
=
−
2
x
−
5
ordered pairs
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Find the missing number so that the equation has infinitely many solutions.
\newline
_
_
_
_
x
−
1
=
−
5
x
−
1
\_\_\_\_x - 1 = -5x - 1
____
x
−
1
=
−
5
x
−
1
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
3
x
−
8
=
‾
x
+
8
3x - 8 = \underline{\hspace{1cm}}x + 8
3
x
−
8
=
x
+
8
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
−
2
x
−
15
=
‾
x
−
15
-2x - 15 = \underline{\hspace{1cm}}x - 15
−
2
x
−
15
=
x
−
15
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
−
4
x
−
11
=
_
_
_
_
x
+
2
-4x - 11 = \_\_\_\_x + 2
−
4
x
−
11
=
____
x
+
2
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
−
16
=
5
x
+
19
\_\_\_\_x - 16 = 5x + 19
____
x
−
16
=
5
x
+
19
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
−
11
=
3
x
−
4
\_\_\_\_x - 11 = 3x - 4
____
x
−
11
=
3
x
−
4
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Find the missing number so that the equation has infinitely many solutions.
\newline
−
4
x
+
5
=
−
4
x
+
‾
-4x + 5 = -4x + \underline{\hspace{1cm}}
−
4
x
+
5
=
−
4
x
+
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
−
3
x
+
2
=
_
_
_
_
x
+
15
-3x + 2 = \_\_\_\_x + 15
−
3
x
+
2
=
____
x
+
15
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
3
x
+
_
_
_
_
=
3
x
+
9
3x + \_\_\_\_ = 3x + 9
3
x
+
____
=
3
x
+
9
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Find the missing number so that the equation has infinitely many solutions.
\newline
_
_
_
_
x
−
1
=
−
2
x
−
1
\_\_\_\_x - 1 = -2x - 1
____
x
−
1
=
−
2
x
−
1
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
3
x
−
11
=
3
x
+
‾
3x - 11 = 3x + \underline{\hspace{1cm}}
3
x
−
11
=
3
x
+
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
−
4
x
−
19
=
‾
x
−
19
-4x - 19 = \underline{\hspace{1cm}}x - 19
−
4
x
−
19
=
x
−
19
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
−
3
x
+
5
=
‾
x
+
5
-3x + 5 = \underline{\hspace{1cm}}x + 5
−
3
x
+
5
=
x
+
5
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
−
2
x
−
20
=
‾
x
−
20
-2x - 20 = \underline{\hspace{1cm}}x - 20
−
2
x
−
20
=
x
−
20
Get tutor help
Find the missing number so that the equation has infinitely many solutions.
\newline
−
5
x
−
5
=
_
_
_
_
x
−
5
-5x - 5 = \_\_\_\_x - 5
−
5
x
−
5
=
____
x
−
5
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
5
x
−
12
=
_
_
_
_
x
−
5
5x - 12 = \_\_\_\_x - 5
5
x
−
12
=
____
x
−
5
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
4
x
−
17
=
_
_
_
_
x
+
12
4x - 17 = \_\_\_\_x + 12
4
x
−
17
=
____
x
+
12
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
−
13
=
5
x
+
5
\_\_\_\_x - 13 = 5x + 5
____
x
−
13
=
5
x
+
5
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
5
x
−
11
=
_
_
_
_
x
+
7
5x - 11 = \_\_\_\_x + 7
5
x
−
11
=
____
x
+
7
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
2
x
+
14
=
_
_
_
_
x
+
1
2x + 14 = \_\_\_\_x + 1
2
x
+
14
=
____
x
+
1
Get tutor help
Find the missing number so that the equation has no solutions.
\newline
3
x
+
13
=
_
_
_
_
x
−
20
3x + 13 = \_\_\_\_x - 20
3
x
+
13
=
____
x
−
20
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Find the missing number so that the equation has no solutions.
\newline
_
_
_
_
x
−
9
=
5
x
+
1
\_\_\_\_x - 9 = 5x + 1
____
x
−
9
=
5
x
+
1
Get tutor help
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