Solve the inequality: five minus one half 𝑥 is greater than or equal to ten for 𝑥.
In order to solve this inequality for 𝑥, we need to first bring the five over to the right-hand side. So let’s go ahead and subtract five from both sides of the inequality. On the left, the fives cancel and on the right ten minus five is five. We’re doing this because we’re trying to isolate 𝑥. We’re trying to get it by itself.
So here we can see that negative one half is being multiplied to 𝑥, so the inverse operation of multiplying would be to divide both sides by negative one half. On the left, the negative one halves cancel. On the right, five divided by negative one half is negative ten. Just a little side note, when you divide by fractions, you’re actually multiplying by the reciprocals. So five divided by negative one half is the same as five times negative two over one. So our numerators, five times two, and we have a negative sign that would be negative ten, and then our denominator one times one is one. So we have negative ten over one, which again is negative ten.
Now since we divide it by a negative, we have to flip the sign of our inequality. So instead of greater than or equal to it will now be less than or equal to. Therefore, 𝑥 is less than or equal to negative ten.