An equation is a problem that needs to be solved. It's like a puzzle with numbers and letters.
An equation uses an equal sign (=) to show that two things are equal. For example:
3x + 5 = 14
This equation is saying that if you take 3 times a number (x) and add 5 to it, you get 14.
To solve the equation, we need to figure out what x is. We can do this by isolating x on one side of the equation. Here's how we can do it:
First, we can subtract 5 from both sides of the equation:
3x + 5 - 5 = 14 - 5
This simplifies to:
3x = 9
Now we need to get x by itself, so we'll divide both sides by 3:
3x/3 = 9/3
This simplifies to:
x = 3
So, we solved the equation! We figured out that x is equal to 3.
Sometimes equations can be more complicated, but the idea is the same. We need to do the same thing to both sides of the equation to keep it balanced and solve for the unknown variable.
Sometimes equations have more than one solution. For example:
x^2 = 16
This equation is saying that if you square a number (x) you get 16. There are two possible solutions for this equation:
x = 4 or x = -4
Both 4 and -4 squared equal 16.
And sometimes equations have no solution. For example:
x + 5 = x - 3
This equation is saying that if you add 5 to a number (x) you get the same thing as if you subtracted 3 from the same number (x). But there's no number that satisfies this equation, so there is no solution.