You're not bad at algebra.
You were taught it wrong.

What x actually is

x is a placeholder. That's it. It's a box with a label on it, sitting where a number should go. We use x because we don't know the number yet — but we know things about it. "x + 3 = 7" just means: "some number, plus 3, equals 7." Your job is to figure out what number belongs in that box.

Why people get confused: They think x is something mysterious. It's not. It's just a number we haven't found yet.

Solving an equation — the balance rule

An equation is a scale. Both sides weigh the same. Whatever you do to one side, you must do to the other — or the scale tips and the equation breaks.

To solve x + 3 = 7, subtract 3 from both sides. Left side: x + 3 − 3 = x. Right side: 7 − 3 = 4. So x = 4. You didn't guess — you moved pieces around while keeping both sides equal.

The rule: same operation, both sides, every time.

What a graph is showing you

A graph is just a picture of a relationship. If y = 2x, that means "y is always double x." When x is 1, y is 2. When x is 3, y is 6. Plot those points and you get a line. The line is showing you every possible pair of numbers that makes the relationship true.

Slope tells you how steep that line is — how fast y changes when x moves. A slope of 2 means: every time x goes right by 1, y goes up by 2.

y = mx + b — the line equation

m is the slope — how steep. b is the y-intercept — where the line crosses the vertical axis (when x = 0, y = b). If someone gives you m and b, you can draw the line. If someone gives you two points, you can find m and b.

Every straight line on a graph can be described with this equation. Once you understand what m and b do, you can read a line like a sentence.

Distributing — why you can't skip it

When you see 3(x + 4), you cannot just write 3x + 4. The 3 multiplies everything inside the parentheses. 3(x + 4) = 3x + 12. Think of it like a delivery truck — everything in the package gets touched.

The distributive property: a(b + c) = ab + ac. Every time. No exceptions. Skipping the distribution is one of the most common algebra errors on every test.

Factoring — distribution in reverse

If distributing is unpacking, factoring is repacking. x² + 5x + 6 looks complicated. But it factors into (x + 2)(x + 3) — two simpler pieces multiplied together. To check: distribute it back out and you get x² + 5x + 6. Same thing.

Why factor? Because once something is factored, you can set each piece equal to zero and solve. (x + 2)(x + 3) = 0 means either x = −2 or x = −3. Two answers, found by splitting one hard problem into two easy ones.