The word "equation" sounds intimidating, but the idea behind it is exactly like a balance-scale game. A two-pan balance stays level when both sides weigh the same. Now say one side has an unknown weight (x) mixed in. Keep the scale level while removing the same amount from both sides, or dividing both sides by the same ratio, and eventually you can figure out exactly how much x weighs. That's what it means to "solve" an equation.
The rule at work here is called the properties of equality. An equation (a statement that both sides are equal) stays true no matter whether you add, subtract, multiply, or divide both sides by the same number. Take the equation 3x + 4 = 19: first subtract 4 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. As long as you remember to always do "the exact same thing to both sides" so the scale never tips, you can work through any equation step by step.
Why solve in this particular order — constant term first, coefficient last? Actually, the order doesn't change the answer. It's just a widely used convention to clear the constant term first, getting the equation into the form "a multiple of x = some number," and then divide by the coefficient last to leave x by itself, because it cuts down on calculation mistakes and is easier to follow. Even when you later solve more complicated equations (with the variable on both sides, or with parentheses), this same big-picture flow — "simplify it down first, then divide at the end" — still applies.
Equations show up anywhere you need to find an unknown value. How many items you can buy to exactly hit a budget, how many minutes until two people meet, how many hours until a car reaches its destination — all these kinds of problems can be written as equations. The ability to name the unknown x and turn a situation into an expression is a powerful tool for converting a complicated word problem into something you can actually calculate.
When studying this with kids, actually putting objects on a real scale (or a drawing of one) works really well. Using a few bags of candy plus loose pieces, pose a problem like "2 bags plus 3 loose candies weighs the same as 11 loose candies — how many candies are in one bag?" and have them work it out by physically removing items with their hands. The feel for "removing the same amount from both sides" sticks much more firmly this way than solving with numbers alone.
On our activity page, you can solve randomly generated equations directly on a scale. Enter a value to subtract or divide by and press "Apply" to clear the scale one step at a time as you work toward the value of x, and press "Next Problem" to keep tackling new equations. Watch the blocks disappear from the scale one by one, and see exactly what each step of solving an equation is actually doing.