Rewrite 𝑥 over six is less
than negative two so that only 𝑥 appears on the left-hand side.
We have 𝑥 over six is less
than negative two. Before we go any further, it’s
really helpful for us to think about how we multiply and divide
inequalities. When we’re multiplying or
dividing with positives, the signs stay the same. And we do the same operation to
both sides. When we’re multiplying or
dividing with negatives, the sign is flipped. And we multiply or divide by
the same thing on either side.
We’re trying to get 𝑥 by
itself on the left-hand side. Currently, on the left, there
is 𝑥 divided by six. And to get rid of 𝑥 divided by
six, we need to multiply by six. Six is a positive value, which
means our sign won’t change. But we’ll still need to
multiply by the same amount on both sides. 𝑥 divided by six times six
equals 𝑥. And negative two times six
equals negative 12. And so we see that 𝑥 is less
than negative 12.
If we wanted to graph that on
our number line, we would have an open circle. And the arrow would go to the
left. If we want to check if this is
true, we can plug in a value that is less than negative 12 into the original
inequality. I’m gonna choose negative
18. I know that negative 18 is less
than negative 12, and it’s divisible by six. Negative 18 divided by six is
negative three. And it is true that negative
three is less than negative two, which confirms 𝑥 is less than negative 12.