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Welcome! Today we are going to explore linear equations, which are just like playground balance scales.
An equation is a mathematical statement showing that two things are perfectly equal. Think of it like a scale in balance: whatever value is on the left side must weigh the exact same as the value on the right side.
In algebra, we use a letter like 'x' to represent a mystery number. If we have 'x + 3 = 7', it means some unknown number plus 3 equals 7. To find our mystery number, we want to get 'x' all by itself on one side of the scale.
To keep the scale balanced, whatever operation you do to one side, you must do to the other side! If we subtract 3 from the left side to leave 'x' alone, we must also subtract 3 from the right side. This leaves us with 'x = 4'.
Solve for y in the equation: y - 5 = 8
- Look at the equation: y - 5 = 8. Our goal is to get 'y' by itself.
- Identify the operation happening to 'y'. Here, 5 is being subtracted from it.
- Perform the opposite (inverse) operation to undo the subtraction. The opposite of subtracting 5 is adding 5.
- Add 5 to both sides of the equation to keep the scale balanced: y - 5 + 5 = 8 + 5.
- Simplify both sides: y = 13.