Algebra Solved Master Equations with Trial and Error! #math #maths #algebra #equations

Added: 2026-05-23

[00:00:00]If 4 to the third power is equal to 64 and 4 to the 3x - 6 power is equal to 64, well then 3x - 6 must be equal to 3.

[00:00:10]So, let's go ahead and set this uh these two things equal to one another and let's do this right here. Okay, so 3x - 6 is equal to 3. Now, even if you didn't know basic algebra, what you could do is just start plugging in numbers here, right? So, hopefully you understand what 3x means. This means 3 multiplied by some number. So, you might be able to, you know, plug in some numbers here. X is equal to 1. Well, let's see here, that'll be 3 * 1. So, 3 * 1 - 6, no, that's going to give me a -3. That's not equal to 3. How about 3 * 2? Well, 3 * 2, that's going to be 6 - 6, that'll be 0. No, that's not going to work. How about 3? 3 * 3 is 9. 9 - 6 is 3. Oh, that looks pretty good to me. So, 3 is the correct answer. Now, if you have some basic algebra skills, you don't have to be an expert in algebra, you could solve this equation for x. So, let's go and do that right now. All right, so you can see I've already done this work. So, 3x - 6 is equal to 3. So, what we need to do is add 6 to both sides of the equation and then we're going to add down in a column manner. Now, if you need some review with basic linear equations, I'll give you some suggestions here in a second, but let's go ahead and finish this up. So, 3x plus nothing is 3x. -6 + 6 is 0, so we don't need to write that.

[00:01:33]And then 3 + 6 is of course 9. All right, so we have 3x is equal to 9 and now we can solve this equation for x by dividing both sides of the equation by 3, which of course is 9 / 3, which is 3.

[00:01:47]Now, we kind of figured this out over here because we were kind of plugging in some numbers and seeing which one worked. So, again, even if you didn't um remember how to solve basic algebraic equations, if you just kind of use some common sense and trial and error, well, you figured this out. Okay, so that is the correct answer.