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Original Question
A student’s work to solve an equation is shown. 1 8 ( 40 x + 16 ) = 9 x − 7 ( 2 x − 1 ) − 5 5 x + 2 = 9 x − 14 x + 7 − 5 5 x...Question
A student’s work to solve an equation is shown.
1
8
(
40
x
+
16
)
=
9
x
−
7
(
2
x
−
1
)
−
5
5
x
+
2
=
9
x
−
14
x
+
7
−
5
5
x
+
2
=
5
x
+
2
2
=
2
8
1
(40x+16)=9x−7(2x−1)−5
5x+2=9x−14x+7−5
5x+2=5x+2
2=2
Select the options that make the following statements true.
The student solved the equation
because the original equation has
1
8
(
40
x
+
16
)
=
9
x
−
7
(
2
x
−
1
)
−
5
5
x
+
2
=
9
x
−
14
x
+
7
−
5
5
x
+
2
=
5
x
+
2
2
=
2
8
1
(40x+16)=9x−7(2x−1)−5
5x+2=9x−14x+7−5
5x+2=5x+2
2=2
Select the options that make the following statements true.
The student solved the equation
because the original equation has
Answers
GPT-4o mini
The statements can be completed as follows:
The student solved the equation **correctly** because the original equation has **infinitely many solutions**.
This conclusion is drawn from the final results of the student's work, where they simplified to the equality \(5x + 2 = 5x + 2\). This indicates that the left-hand side is always equal to the right-hand side for any value of \(x\), leading to the conclusion that there are infinitely many solutions to the original equation.
The student solved the equation **correctly** because the original equation has **infinitely many solutions**.
This conclusion is drawn from the final results of the student's work, where they simplified to the equality \(5x + 2 = 5x + 2\). This indicates that the left-hand side is always equal to the right-hand side for any value of \(x\), leading to the conclusion that there are infinitely many solutions to the original equation.