Solving for a Variable on One Side Using Addition and Subtraction with Fractions #5

[One speaker] 

[Solve for the variable: ]

Narrator: For the variables - so we are going to try isolate J. We’re gonna solve for J, but first we need to find the additive inverse of 4/3. And we know that 4/3 plus something will equal zero. Well, in this case, that is negative 4/3. Our additive inverse is negative 4/3.
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So we are going to subtract 4/3 from this side. We can also write this as plus a negative 4/3. But remember that that will give us the same thing as subtracting 4/3, so I’m going to write it as minus 4/3, and we’re gonna do that to this side as well. We’re running out of room a little bit, But we will rewrite it.

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So let’s rewrite this as negative 4/3 minus 4 equals J. We have plus 4/3 minus 4/3, which is going to equal zero, so we just have J on the right-hand side.

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And on the left side, we can rewrite this as negative 4 over 3 minus 4 over 1, and that’s equal to J. But remember that we need to find a common denominator, and the least common multiple between 3 and 1 is going to be 3.

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We can multiply 4 over 1 by 3 over 3, and that’s going to give us negative 4/3 minus 12 over 3, and that’s equal to J.

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Now, negative 4 minus 12 is negative 16 over 3. So we found J is negative 16 over 3. But we can plug this back into our equation here and check our work [boxes off the answer and draws an arrow pointing to the j in the original equation]. Let’s do that over here.

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We have negative 4 is equal to J, but we found J to be negative 16 over 3. So negative 16 over 3 plus 4/3. We have a common denominator already. Negative 16 plus 4 is negative 12 over 3, and negative 12 divided by 3 is equal to negative 4.

[Draws check mark next to boxed answer.]

So yes, we found the right answer.

[End of Video]