Question Video: Solving Two-Step Linear Equations over the Set of Integers Mathematics • 7th Grade

Find the solution set of (π‘₯/4) βˆ’ 3 = βˆ’5 in β„€.

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Video Transcript

Find the solution set of π‘₯ over four minus three equals negative five in the set of all integers.

First, we remember that this symbol is the set of all integers. And then, we can turn our attention to solving for π‘₯. If π‘₯ over four minus three equals negative five, we want to try to isolate π‘₯, to get π‘₯ by itself. And the first thing we should do in order to do that is add three to both sides. Once we do that, we’ll get π‘₯ over four is equal to negative two because negative five plus three equals negative two.

We know that π‘₯ over four means π‘₯ divided by four. Some value divided by four equals negative two. To find out what that value is, we need to do the opposite. If π‘₯ is being divided by four, we need to multiply both sides of the equation by four, like this. Four times π‘₯ over four equals π‘₯, and negative two times four equals negative eight. At this point, we should check and see if that’s true.

Is negative eight divided by four minus three equal to negative five? Negative eight divided by four is negative two. And negative two minus three is negative five. This means that π‘₯ is equal to negative eight. But here our solution needs to be given as a set notation. That’s the curly brackets. And the solution set for this equation is just negative eight.

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