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Video: Solving One-Variable Equations

Kathryn Kingham

I think of a number, multiply it by 2 and subtract 1 from the answer. The result is 9. What is my number?


Video Transcript

I think of a number, multiply it by two, and subtract one from the answer. The result is nine. What is my number? The best way to solve this problem is to take all of these words and turn them into an equation.

We’ll start at the beginning of the problem and then we’ll work through it by adding each piece of the equation, beginning with I think of a number.

That’s a number that we don’t know. It’s what we’re trying to solve for. We need to choose a variable for this number. How about 𝑛? I think of a number, we’re gonna call that number 𝑛.

We’ll keep moving through the problem. The next statement is that we multiply that number by two. For us that means we’re gonna multiply 𝑛 by two.

I could write 𝑛 times two, but two 𝑛 is the simplest way to write that. And I write it this way because when we put a number in front of a variable, we know that it means multiplication.

What happens next? Subtract one from that answer. That part is pretty simple. Now we have two 𝑛 minus one. Moving on through the question, our question tells us the result is nine. We represent that by equal to nine.

As we’re moving on through the question, it’s now just asking what is the number. That means we need to solve for 𝑛. Let’s solve this two-step equation.

We’ll start by adding one to both sides of our equation. Two 𝑛 minus one plus one equals two 𝑛. Nine plus one equals 10.

Now we know that two times our number equals 10. Now I’m going to divide both sides of our equation by two. Two 𝑛 divided by two equals 𝑛, and 10 divided by two equals five.

The missing number is five. But if you weren’t sure if that was the case and you wanted to check, we can take our five and plug it back into our original equation. Does two times five minus one equal nine? Two times five equals 10; 10 minus one does equal nine, which confirms our final answer: 𝑛 equals five.