Question Video: Solving Linear Inequalities by Multiplying by a Negative Number Mathematics • 7th Grade

If π§ + 1 β€ β9, then βπ§ οΌΏ.

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Video Transcript

If π§ plus one is less than or equal to negative nine, then negative π§ blank.

We have the inequality π§ plus one is less than or equal to negative nine. In order for us to find what negative π§ would be equal to, we first need to find π§ by itself. We can do this by subtracting one from either side of this inequality. And we see that π§ is less than or equal to negative 10. If we want to know something about negative π§, we could multiply the entire inequality by negative one. But we have to remember that when weβre multiplying inequalities by negative values, we need to flip the sign. And that means weβll have to change it from a less than or equal to to a greater than or equal to.

After that, we multiply through by negative one just like we would in an equation so that we have negative π§. And then, negative one times negative 10 is positive 10. If π§ is less than or equal to negative 10, then negative π§ will be greater than or equal to positive 10 .