Solve for x in the equation: 5x - 2 = 3.

To solve the equation (5x - 2 = 3), you will follow a series of algebraic steps that help isolate (x).

First, add 2 to both sides of the equation to eliminate the -2 on the left side. This gives you:

[

5x - 2 + 2 = 3 + 2

]

Simplifying both sides results in:

[

5x = 5

]

Next, to isolate (x), divide both sides of the equation by 5:

[

x = \frac{5}{5}

]

This simplifies to:

[

x = 1

]

Thus, the solution to the equation (5x - 2 = 3) is (x = 1).

The answer being 1 is confirmed as it satisfies the original equation when substituted back in. If you replace (x) in the equation with 1:

[

5(1) - 2 = 3

]

This simplifies to:

[

5 - 2 = 3

]

Thus, (3 = 3) holds true. This demonstrates that 1 is indeed the correct solution for (