An equation makes a claim
An equation has two sides joined by an equals sign, like x + 3 = 7. It is really a claim: it says the left side and the right side name the same number. The catch is that one side contains a letter — a variable standing for an unknown number — so whether the claim is true depends on what that letter equals.
A solution is any value of the variable that makes the claim true. For x + 3 = 7, the value x = 4 works because 4 + 3 really is 7. The value x = 5 is not a solution, because 5 + 3 = 8, and 8 ≠ 7. Solving means finding every value that turns the equation into a true statement.
Checking by substitution
The single most reliable skill in algebra is checking a solution. To test whether a number is a solution, replace the variable with that number everywhere — this is substitution — then simplify each side separately and see if they match. This works for any equation you will ever meet, so it never lets you down.
Check whether x = 4 solves 2x - 1 = x + 3 Left side: 2(4) - 1 = 8 - 1 = 7 Right side: (4) + 3 = 7 7 = 7 TRUE -> x = 4 is a solution. Now test x = 1 in the same equation: Left side: 2(1) - 1 = 1 Right side: (1) + 3 = 4 1 = 4 FALSE -> x = 1 is NOT a solution.
Linear means one unknown, first power
This track is about linear equations in one variable: equations where the unknown appears only to the first power — no x^2, no 1/x, no sqrt(x). Examples are 3x + 5 = 20 and 7 - 2y = y. Such an equation has exactly one solution, except for two special cases we will meet later. That tidy promise of one answer is what makes the linear case the right place to start.
You can often guess a solution to a simple linear equation, then confirm it by checking. That is a perfectly honest method, and it builds the right instinct. But guessing does not scale to 17x - 4 = 9x + 60, so the next guides teach a method that always works.