Solve each equation. | 4x + 2 | = 5

Question

Accepted Answer

Hello everyone. In this video, we're going to be looking at this practice problem where we want to find X in the equation, absolute value of three X plus seven is equal to nine. And in this problem, you can see that X is inside an absolute value. So we want to think about what the absolute value is doing to the component inside of it. So recall that if we take the absolute value of a number such as a, we get back a But if I take the absolute value of a negative number such as -8, I also get back positively. So notice that in this scenario, the A's had opposite signs going in but the outputs looked exactly the same. So that means that when I'm solving for X inside an absolute value, I have to consider if it's positive or negative on the inside because we don't know because the absolute value once it gets output ID, we get the same output, we have to consider both of these scenarios. So that means that the inside of the absolute value could truly be positive three X plus seven equal to nine. But it could also be negative three acts plus seven is equal to nine. So in order to find all the solutions for X, I need to consider both of these scenarios. So if I start by solving, if the inside was positive, I'll subtract seven from both sides. So it leaves me with three, X is equal to nine minus seven just to, to completely isolate exile divide by three on both sides. So that means the X is equal to two thirds. So that gives me one of the solutions for X. Now we can take a look at if the inside was negative. And you can see I have the negative on the outside here. So I'll go ahead and distribute it. So negative one times three X is negative three X negative one times positive seven is negative seven, that's still equal to nine. And now I'll start to isolate X by adding seven to both sides. So I have negative three, X is equal to nine plus seven, just 16 And to completely isolate x all divided by -3. So it leaves me with X is equal to negative 16/3. You can see that I have two solutions for X. Now. So the absolute value calls me to have two solutions for X X could be negative 16 3rd Or positive 2/3. So he's become my solutions for X. And if you look at the answer choices, you can see answer choice. A also has negative 16/3 and positive two thirds. So hopefully this video helped and see you next time.

Solve each equation. | 4x + 2 | = 5

Key Concepts

Absolute Value

Linear Equations

Case Analysis

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