Solve for x: 5⋅x + 3 = 2⋅x - 3.

To solve the equation (5x + 3 = 2x - 3), the first step is to isolate the variable (x).

Start by eliminating (2x) from both sides of the equation:

[

5x - 2x + 3 = -3

]

This simplifies to:

[

3x + 3 = -3

]

Next, subtract 3 from both sides to further isolate the term with (x):

[

3x = -3 - 3

]

This results in:

[

3x = -6

]

Now, divide both sides by 3 to solve for (x):

[

x = \frac{-6}{3}

]

Simplifying this gives:

[

x = -2

]

Thus, the solution to the equation is (-2.0). This indicates that the value of (x) satisfies the original equation when substituted back in, confirming the correctness of the calculation.

The other potential answers do not satisfy the equation when substituted back, thereby making (-2.0) the only valid solution from the given choices.