Linear Equations and Inequalities
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Solving linear equations. Another linear equation that we have is 4 times x minus 7 equals 4x minus 28. Distributing out this 4, and so make sure the 4 goes to both things, we get 4x minus 28 is equal to 4x minus 28.
If you look carefully, you notice that we actually have the same thing on both sides, this actually has to be true. 4x minus 28 has to equal 4x minus 28 no matter what you plug in, they have to work. We’ll talk bout what that means, but if you didn’t see that, let’s continue on.
We want to isolate our xs, minus 4x minus 4x, our xs disappear all together. -28, add the 28, our 28s disappear-. What we actually end up with is, just zero equals zero. Everything disappeared, leaving us with zero equals zero. This is a true statement. What that actually means is, no matter what we plug in for x, we’ll always get zero equals zero. 4x minus 28 always has to equal 4x minus 28.
What this tells us is, we can actually put in any value of x and this will work. You put in 5, you put in 32, it will always work out. Depending on your teacher, you're going to have to write this a little bit differently, you know some people would just say, all real numbers, you can plug in anything for x, some people could say negative infinity to infinity. It all depends, this is a identity, basically anything we plug in, it’s always going to work.