A student’s work to solve an equation is shown.

Question

​
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 correctly or incorrectly?
because the original equation has no solution,one solution, or infinite solutions?

Answer 1

Based on the work shown by the student, we can analyze the steps taken and the conclusion reached.

1. The original equation simplified down to \( 5x + 2 = 5x + 2 \). This kind of equality indicates that both sides of the equation are identical for any value of \( x \).

2. Since both sides are the same, this indicates that there are infinite solutions to the equation. In other words, no matter what value \( x \) takes, the equation will hold true.

Answer:

• The student solved the equation correctly because the original equation has infinite solutions.