Simplify three-quarters 𝑥 plus five-sevenths minus an eighth 𝑥 plus one-seventh.
Now, in order to simplify our expression, what we wanna do is collect like terms. And like terms are terms that have the same power of 𝑥 in this case. So, we can see we’ve got terms that have 𝑥 to the power of one, or just 𝑥. And then, we’ve got terms without 𝑥. So, to help us understand what we’re gonna do, what I’ve done first of all is drawn a box in orange around all the terms that contain 𝑥.
We can also see that we included the sign before. And that’s because this relates to the term itself. So, we can see that we’ve got three-quarters 𝑥 minus one-eighth 𝑥. Well, if we want to solve this, we want to take one-eighth 𝑥 away from three-quarters 𝑥. We want to make it so that they both have the same denominator. And we can do that by doubling both the numerator and the denominator on our three-quarter 𝑥. And that’s because if we double four, we get eight.
So, if we do that, we get six over eight 𝑥 minus one over eight 𝑥. Well, if we’re gonna subtract these, then because they’re both 𝑥, all we need to do is think about the fractions. So, if we got six-eighths minus one-eighth, we just subtract the numerator. That’s because the denominator is the same. So, this leaves us with five over eight 𝑥. And then, we have five over seven, and it’s positive five over seven, add one over seven. So, we got five-sevenths plus one-seventh. Well, again, because the denominator is the same, all we need to do is add the numerators . So, five add one over seven, which equals six over seven.
So therefore, we got five over eight 𝑥 plus six over seven. So then, we can say that, fully simplified, three-quarters 𝑥 plus five over seven minus one-eighth, or one over eight, 𝑥 plus one-seventh is equal to five over eight 𝑥 plus six over seven. And we know that this is correct because we cannot simply this any further because the two terms contain different powers of 𝑥. Because the first term has 𝑥 to the power of one, and the second term doesn’t have an 𝑥. Or you could think of it as having 𝑥 to the power of zero.