Solving Two-Step Equations Page 3 of 4
Let's try another example. Let's say I have another mystery number. If I divide it by 4 and then I subtract 3 from it, I get 2. What is my number? First, let's write this as an equation. If we call the mystery number x, we could use x/4 to represent dividing the number by 4 and then put the minus 3 after it to show that we subtracted 3 next. This gives us the equation:
When you're solving an equation, the goal is to get the variable by itself. We need to work our way backwards to figure out what x was.
Remember, we divided by 4 first and then subtracted 3. If we go backwards to find x, the first thing we need to do is to undo the subtraction. How do you undo subtracting 3? We need to use the inverse operation to cancel it and add 3 to both sides. Remember to always do the same thing on both sides of the equation so everything stays balanced.
Why do you undo the subtraction first? If you knew what x was and you were using PEMDAS to simplify the expression, you would do the subtraction last. When you're solving, you're working your way backwards to get x by itself. Since addition and subtraction are done last when simplifying, that means they'll be the first things you undo when you're solving an equation.
Now that we've canceled out the minus 3, we're left with x/4 = 5. This means that x is being divided by 4. How do we undo division? We need to use the inverse operation and multiply. If we multiply both sides by 4, it will cancel the division by 4.
Remember to always do the same thing on BOTH sides of the equation. A common mistake is for students to multiply one side and forget to multiply the other side.
How do you check your answer to see if it's right? You plug your answer back in the original equation and see if it works. We need to plug 20 in for x in the original equation and make sure it comes out to 2. If we divide 20 by 4 and then subtract 3, we see that it does come out to 2. This means we have the correct answer.