How do I solve for a variable when it is on both sides like: 5y + 3 = 4y -1?

This is an equation in one unknown or variable y.We solve  the equation  in one unknown  by making the variable  to one side and the known or the number to the other side. We do this by simple operartions like adding the equals to both sides, or subtracting the equals to both sides , or multiplying by the equals both sides , or dividing by the equals(but not by zero) both sides of the equation:

5y+3=4y-1. Here 5y  on the left and 4y on the right are  the unknowns. 3 on left and -1 on the right are the numbers and they are known. To make the unknowns on the left and the knowns on the right with a purpose of making the unknown to be determined through the knowns, we do the following operations , one by one:

Subtract 4y from both sides:

5y+3-4y= 4y-1-4y.

Simplify by collecting the like terms together:

5y-4y+3=4y-4y-1

y+3=-1

Subtract 3 from both sides:

y+3-3=-1-3

Simplify.

y= -4.

Verification:

Substitute  the obtained solution, y=-4 in the original equation and see whether you get the same value on both sides:

Left:5(-4)+3=-20+3=-17

Righr:4(-4)-1=-16-1=-17

Hope this helps.