Solve each equation or inequality. | 4 - 4x | + 2 = 4

Question

Accepted Answer

Hello Everyone in this video we're going to be looking at this practice problem where we want to solve the equation absolute value of six minus six X plus four equals eight for X. So in this case this equation has an absolute value. So we want to consider how the absolute value is affecting are variable X. Or even just the components inside the absolute value. So recall that the absolute value means that the number inside the absolute value could be positive. So we could have positive six minus six X plus four equal to eight. But the absolute value makes any number inside of it positive. So that means that 6 -6 X could also be negative. So it could be negative 6 -6 x Plus four equal to eight. So in order to find the correct solutions for X we want to consider both of these possibilities. So if if the components inside the absolute value were positive we would have six minus six X plus four equal to eight. I can combine the six and the four to give me 10 minus six X is equal to eight. All subtract 10 from both sides in order to isolate X. So I have negative six X. Is equal to negative two because eight minus 10 is negative two. and finally I'll divide by -6. So that gives me X. is equal to two divided by six. I can simplify too negative two divided by negative six. I can simplify to positive one third. That gives me one solution for X. But I still need to consider this second scenario. So first I'll distribute this negative one to the six. So this gives me negative six negative one to the negative six. X. Gives me positive six sex and I still have the plus four equal to eight. And now when I combine the negative six and the four I have negative six plus four which gives me negative two plus six sex is equal to eight. And in order to isolate X once again I'll add two to both sides. Leaving me with six X is equal to 10. All divided by six. That means X is equal to 10 divided by six, which I can simplify to five thirds. So now I have two solutions for X. So there's not only one solution for X in this equation because of the absolute value X could be one third or five thirds. So this becomes my final solutions for this problem and you can see that answer choice B also has one third and five thirds. So hopefully this video helped and see you next time

Solve each equation or inequality. | 4 - 4x | + 2 = 4

Key Concepts

Absolute Value Equations

Isolating the Absolute Value Expression

Solving Linear Equations

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