Answer:
The main objective of any equation is to single out the parameter you're trying to solve for for on one side, and any other parameters and constants on the other (i.e., x = 10, y = -2, z = b - 5).
Therefore, we're looking to move terms from one side to the other until we're left with the parameter we're solving for on one side of the equation, and everything else on the other. We do this by using opposite operators for the different terms.
For example, if we had x + 3 = 7, we would move the 3 over by subtracting 3 from both sides of the equation:
[tex]x + 3 =7 \text{ // -3}\\x + 3 - 3 = 7 - 3\\x = 4[/tex]
In your case, in order to move -10 to the other side (in the equation 5x - 10 = 15), you would want to add 10 to both sides, thus removing -10 from the left side of the equation.
[tex]5x - 10 = 15 \text{ // +10}\\5x - 10 + 10 = 15 + 10\\5x = 25[/tex]
Finally, to single out x on the left side of the equation, we would want to remove its coefficient (5). To do this, we can divide both sides of the equation by the coefficient.
[tex]5x = 25 \text{ //}\div5\\\frac{5x}5 = \frac{25}5\\\\\to x = 5[/tex]
