<u><em>Answer:</em></u>
The given equation has <u>infinite number of solutions</u>. This means that <u>any real number</u> can be considered a solution to the given equation.
Since the given replacement set {2,3,4,5} consists of real numbers, therefore, the whole set is considered as a solution to the given equation.
This is because, when solving the given equation for x, we will end up with 0 = 0, this means that whatever the value of x is, both sides of the equation will always be equal.
<u><em>Explanation:</em></u>
To solve for x, we need to isolate the x on one side of the equation.
<u>This can be done as follows:</u>
3 + 2x = 2x + 3 (subtract 3 from both sides)
2x = 2x (subtract 2x from both sides)
0 = 0
This means that whatever, the value of x is, both sides of the equation will be equal. This means that all real numbers are considered a solution for this equation.
<u>Let's verify this using the given replacement set {2,3,4,5}:</u>
<u>For x = 2: </u>
Left hand side: 3 + 2(2) = 3 + 4 = 7
Right hand side: 2(2) + 3 = 4 + 3 = 7
Both sides are equal.
<u>For x = 3:</u>
Left hand side: 3 + 2(3) = 3 + 6 = 9
Right hand side: 2(3) + 3 = 6 + 3 = 9
Both sides are equal.
<u>For x = 4:</u>
Left hand side: 3 + 2(4) = 3 + 8 = 11
Right hand side: 2(4) + 3 = 8 + 3 = 11
Both sides are equal.
<u>For x = 5:</u>
Left hand side: 3 + 2(5) = 3 + 10 = 13
Right hand side: 2(5) + 3 = 10 + 3 = 13
Both sides are equal.
Hope this helps :)
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