The rule for rewriting an absolute value equation without absolut...

Question

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars:
If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84.

|4x - 3| = |4x - 5|

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to solve the absolute value equation the absolute value of seven X minus 11 is equal to the absolute value of seven X minus three. So in this case we're working with absolute values and recall that an absolute value gives whatever numbers inside as positive. So in reality it could really be negative or positive meaning that if we have an absolute value of U. Equal to a. You could really be A. Or it could be negative A. So we're going to keep that in mind when we're solving for this equation. So we have seven x -11 and that could equal positive seven X -3. But we also need to account for if it's negative And if it's negative we have seven X -11 equal to -7 X -3. So now using both of these equations we can try to find the solution for X. So I'm gonna move all the X. Values to one side. So I have I'm gonna add 11 subtract seven X from both of these. You can see that I'm left with zero is equal to eight for the positive. So this makes no sense because zero does not equal eight and we're not left with any access. So it's not telling us the value effects. So now we're going to solve for the negative part where we have seven x minus 11 is equal to redistribute the negative negative seven X plus three. So now I'm gonna add seven x. And at 11 to both sides. So now we have 14 X. Is equal to 14. So that leaves me with X. is equal to one. So now I have this solution that is saying X is equal to one. And in order to make sure that the solution is good we can plug it back into our equation Where we have seven X -11 is equal to seven X - and both of those have absolute value functions. So I plug in one. I have seven Times 1 -11 is equal to seven times 1 -3. So now I have 7 -11 is equal to 7 -3. And in this case On the left hand side I have negative four and on the right hand side I have four. But because they both are under absolute values this negative four becomes positive for. So now I have four is equal to four and because four is equal to four is a true expression, I know that X equals one is a true solution for this equation. So that becomes my final answer. And you can see that that aligns with answer choice C. X. Is equal to one. So hopefully this video helped and see you next time

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