Solve the following linear inequalities and write the solution in interval notation.−56x<3-\frac56x<3

-\frac{18}{5}"\u003ex\u003e−185x\u003e-\frac{18}{5}

Solve the following linear inequalities and write the solution in interval notation. − 5 6 x < 3 -\frac56x<3

we're asked to solve the linear inequality and write the solution in interval notation. So this is negative five sixth x is less than three. So we're working with a fraction coefficient here. Our goal is to get this x all by itself, which we can do by multiplying by the reciprocal of this fraction in order to get it to cancel. Now keep in mind that this fraction is also negative, so we're going to be multiplying specifically by a negative value and we're just flipping that fraction. So if this is negative five sixths, we can cancel this by multiplying by negative six over five, just flipping that fraction. Now whatever I do to one side, I have to do to the other. So I'm gonna multiply three by negative six over five as well. Now since we are working with an inequality and we are multiplying by a negative value, that means we have to flip our inequality symbol when we do this multiplication. Otherwise, our answer will be wrong. So these are going to cancel out just leaving me with x, but I need to flip my inequality symbol. Right now it's less than. I want to make it greater than. So I have x is greater than three times negative six over five. We can treat this three as a fraction as just three over one. Multiplying our numerators across, three times negative six gives me negative eighteen and one times five multiplying denominators across is going to give me five. Now, this fraction doesn't reduce any further but this is my solution here that x is greater than negative 18 over five. Now, we can write this in interval notation here thinking about values that are greater than this negative 18 over five. So starting at negative 18 over five, spanning on to infinity. Now both of these values are enclosed in parentheses rather than square brackets because this is just greater than, not greater than, or equal to so we don't wanna include this value. And infinity can never be included because it's not an actual value, so we always use parentheses there. Now if you have any questions, feel free to let us know, and I'll see you in the next problem.

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Solve the following linear inequalities and write the solution in interval notation.−56x<3-\(\frac\)56x<3

다음 시청

Solve the following linear inequalities and write the solution in interval notation.
$negative five sixths x is less than 3$