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
correctly
incorrectly


no solution
one solution
infinitely many solutions

Answer 1

The student's work shows that they arrived at the equation \( 5x + 2 = 5x + 2 \), which is an identity; this means that the left-hand side is equal to the right-hand side for all values of \( x \).

Thus, we can conclude the following:

- The student solved the equation **correctly**.
- The original equation has **infinitely many solutions**.

So the correct selections are:
- The student solved the equation **correctly**.
- The original equation has **infinitely many solutions**.