Solving equations with a balance

Hello, and welcome to Myriora Maths! Three x, plus four, equals nineteen. What is x? Today, we'll solve it with a balance.

Why do we need equations? Here's a puzzle. You had nineteen pounds. You bought three comics, all the same price, and you have four pounds left. How much was each comic? That's exactly the equation three x, plus four, equals nineteen, where x is the price of one comic.

An equation is like a balance. Both sides weigh exactly the same. On the left, there are three bags, each holding x marbles, plus four loose marbles. On the right, there are nineteen loose marbles.

Here's the golden rule: whatever you do to one side, do to the other, or the balance tips. So let's take four marbles off both sides. Now three bags balance fifteen marbles.

Three bags, fifteen marbles. Share the fifteen into three equal groups. Five in each. So x equals five! Each comic cost five pounds.

Always check. Three times five is fifteen. Plus four is nineteen. It balances!

Let's try one together. x, plus five, equals twelve. What should we take from both sides? Say your answer out loud!

Take five from both sides. That leaves x on its own: x equals seven. Check: seven plus five is twelve. It balances!

Let's try one more. Two x, minus three, equals eleven. This time, add three to both sides. Two x equals fourteen. Now divide both sides by two. X equals seven.

Here's a question that catches lots of people. Three x, plus four, equals nineteen. Some people take four from the left side only, and write three x equals nineteen. But then the balance tips! Take four from both sides: three x equals fifteen.

Your turn! Five x, plus two, equals thirty-seven. What is x? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Take two from both sides: five x is thirty-five. Divide both sides by five: x is seven. Check: five times seven, plus two, is thirty-seven!

Quick review. An equation is a balance. Do the same thing to both sides. Undo the adding first, then the multiplying. And always check your answer. See you next time!