Given that 𝑥 times six plus nine is equal to negative seven times six plus negative seven times nine, find the value of 𝑥.
Let’s look at two different ways we could solve this. First, we have 𝑥 times six plus nine is equal to negative seven times six plus negative seven times nine. And we can go ahead and calculate these operations. Six plus nine is 15. Negative seven times six is negative 42. Negative seven times nine is negative 63. And then we can add negative 42 and negative 63, which gives us that 𝑥 times 15 is equal to negative 105. From there, we’ll need to divide both sides of this equation by 15, and we’ll see that 𝑥 equals negative seven.
But let’s look at a second method. If we look at this equation, on the right side, we have two terms that have a factor of negative seven. And that means we can undistribute this negative seven. If we do that, the right-hand side of this equation becomes negative seven times six plus nine, and the left-hand side of the equation is 𝑥 times six plus nine. We’re saying some number times six plus nine has to be equal to negative seven times six plus nine. And that number will have to be negative seven.
Using the distributive property in this method allowed us to simplify without having to calculate each of the values. But both methods show that 𝑥 must be equal to negative seven.