Solve each equation or inequality. |8 - 3x| - 3 = -2

Question

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where I want to solve for X. In the equation absolute value of nine x minus four minus six is equal to negative five. So in this case we're working with an absolute value. So we want to think about what the absolute value is doing to the components inside of it which in this case is nine x minus four. So in this case nine x minus four could be positive. So I would have positive nine X minus four and the negative six and negative five are unaffected because they're not inside the absolute value. But nine x minus four could also be negative because recall that the absolute value makes any negative any negative component inside of it positive. That means that negative nine x minus four could be negative. So when I'm finding the solutions for X I want to take that into account to make sure that I find all solutions of X. And again the negative six and negative five are unaffected. So I can start by solving this first equation and I can combine the negative four. And the negative six. Leaving me with nine x minus 10 is equal to negative five. And in order to start isolating X. I'll add 10 to both sides. Leaving me with nine X is equal to negative five plus 10 is positive five, dividing by nine X. Is equal to five divided by nine. So that is one of my solutions for X. And now I can look up the second equation where nine X minus four is negative. So first I'll distribute this negative so negative one times nine X is negative nine X negative one times negative four is positive for and again the negative six and negative five are unaffected. But now I can combine the four and the six. So that leaves me with nine X positive four minus six is negative two, still equal to negative five. And to begin isolating X, I'll add two to both sides. Leaving me with negative nine X is equal to negative five plus two is negative three And in order to completely isolate x all divided by -9. So X is equal to negative three divided by negative nine. I have two negatives so that makes it positive and I can simplify three divided by nine to be one third. So you can see here that because of the absolute value X actually has two solutions, so X could be positive one third Or positive five nines. So this becomes my final solutions for this equation and you can see that answer choice. A also has one third and five divided by nine. So hopefully this video helped and see you next time

Solve each equation or inequality. |8 - 3x| - 3 = -2

Key Concepts

Absolute Value Equations

Isolating the Absolute Value Expression

Solving Linear Equations

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