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

Find the solution set of 7π‘₯ + 11 = βˆ’24 in β„€.


Video Transcript

Find the solution set of seven π‘₯ plus 11 equals negative 24 in the set of all integers.

We remember that this symbol that looks a little bit like a Z is the set of all integers. We know that seven π‘₯ plus 11 equals negative 24. And the solution set will be the values for π‘₯ that makes seven times π‘₯ plus 11 equal to negative 24. In order to solve for π‘₯, we need to get π‘₯ by itself. And the first thing we can do is subtract 11 from both sides of the equation. If we subtract 11 from both sides, it keeps this equation balanced.

Seven π‘₯ plus 11 minus 11 equals seven π‘₯. And negative 24 minus 11 equals negative 35. And now, we have seven π‘₯ equals negative 35. It means seven times some number equals negative 35. In order to undo that multiplied by seven, we need to divide both sides of this equation by seven. Seven π‘₯ divided by seven equals π‘₯. And negative 35 divided by seven equals negative five. This means that when we multiply seven by negative five and then add 11, we should get negative 24.

Seven times negative five is negative 35. Is negative 35 plus 11 equal to negative 24? It is. And so, we found the value that π‘₯ must be is negative five. We should be careful here because our question is asking us for a solution set. And that means we’ll need to use the curly brackets. But the only integer, the only value, for π‘₯ that makes this statement true is negative five. And that means that’s the only value that goes into the solution set. The solution set of this equation is negative five.

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