Solve the equation negative seven 𝑥 plus nine equals negative 22 plus four 𝑥.
In order to solve our equation for 𝑥, we need to get 𝑥, our variable, to one side of the equation and all of the other numbers, which are called our constants, to the other side of the equation. Essentially, we are isolating 𝑥 to be all by itself.
In order to do that, we need to put all of the 𝑥s to one side. Let’s go ahead and move the four 𝑥 over to the left side. Since four 𝑥 is positive, in order to move it, we need to subtract four 𝑥. That way, it disappears on the right-hand side.
Subtracting four 𝑥 from both sides of our equation means it’s no longer on the right-hand side of our equation, and negative seven 𝑥 minus four 𝑥 is negative 11𝑥. And now we should bring down the rest of our equation.
Now we need to move our constants or our numbers to the right-hand side of the equation. First we need to get rid of the nine. In order to eliminate nine, we must subtract nine from itself. That means we have to subtract it from both sides of the equation.
This makes the nines cancel, and negative 22 minus nine is negative 31. Therefore, right now, we have negative 11𝑥 equals negative 31. Negative 11 is being multiplied to 𝑥, so the opposite will get rid of it. So instead of multiplying by negative 11, we need to divide both sides by negative 11.
Dividing both sides by negative 11, this results in 𝑥 equals negative 31 over negative 11. This can be reduced because two negatives create a positive; a negative divided by a negative is a positive number.
Therefore, 𝑥 equals positive 31 over positive 11 because a negative number divided by a negative number results in a positive number. Our final step is to make sure 31 divided by 11 does not reduce, meaning they both don’t have a common factor that we could take out.
Since 11 is prime, meaning it’s only divisible by itself and one, and 11 does not go in evenly to 31, then 31 elevenths does not reduce, so our final answer 𝑥 equals 31 over 11.