Solve each equation. | 5/ x-3 | = 10

Question

Accepted Answer

Hello everyone. In this video, we're gonna be looking at this practice problem where we want to solve the equation. Absolute value of nine divided by X minus seven is equal to 14 for X. So in this case, we're working with an absolute value equation. So we want to think about what the absolute value is doing to the numbers inside of it. So when we have an absolute value, recall that the inside number could be positive. So we could have positive nine divided by X minus seven is equal to 14. But the numbers inside the absolute value could also be negative because recall the absolute value makes any negative number positive. So we could have negative nine divided by X minus seven equal to 14. So when solving this equation for X, we have to consider both of these scenarios. So I'm gonna start by solving if the absolute value was positive. So I can do that by multiplying by X minus seven. So when I multiply X minus seven to both sides, it cancels on the left hand side, leaving me with nine is equal to 14 times X is 14, X minus 14 times seven, which is 98 in order to isolate X, I'm gonna add 98 to both sides. So that leaves me with 107 is equal to 14 X and I'll divide by 14, says X is equal to 107 divided by 14. So that's my final isolation for if the inside of the absolute value was positive. And now I need to look at if the inside was negative. So I'll go ahead and distribute this negative inside the parentheses. So say this is negative nine divided by X minus seven. And I'll begin to isolate X again by multiplying by X minus seven. So now I have negative nine is equal to 14 times X and 14 times seven which is 98. And once again, I'll add 98 to both sides. So negative nine plus 98 is 89. We start 14 X on the right hand side. So I'll divide by 14 to isolate X. So that means that X is equal to 89 divided by 14. And you can see because of the absolute value X actually has two solutions. It could be 89 divided by 14 or it could be 107 divided by 14. So this becomes my final answer with this practice problem. And you can see that answer choice. A also has 89 divided by 14 and 107 divided by 14. So hopefully this video helped and see you next time.

Solve each equation. | 5/ x-3 | = 10

Key Concepts

Absolute Value

Equations and Solutions

Rational Expressions

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