Week12- Precalc11

It’s been a very busy but full week. We finished our chapter5, had a test and started to learn chapter8. We learned how to draw an absolute value function and how to solve the absolute value equations graphically and algebraically.
I want to remind myself of something that needs to be paid attention in about chapter5. I always confused myself when solving inequalities, do I need to sketch the whole graph or just draw the number line when solving the problems? But now I think I understand, when it only has one variable, for example, x, I can just use the number line; when it has both x and y, I should graph the function first, that way I can know the scale visually to solve it. I think that’s all I need to let myself notice for this unit.
Then for chapter8, we should solve the absolute value equation by separating it into two equations to get 1/2/3/4 solutions (every equation has a different amount of solutions from each other, depending on when two lines or parabolas bump into each other.)
For instance, x+8= the absolute value of4x+6, so we can regard it as” x+8=4x+6″ and “x+8=-(4x+6)”.Then we solve these two equations and we get that x=2/3 orx=-14/5.