Inequalities

An equation asks which number makes both sides equal. An inequality asks which numbers make one side SMALLER than the other — and usually there are infinitely many of them.

You solve it exactly like an equation: to get x on its own in 6x < 47, divide both sides by 6, giving x < 7.83…

So every number below 7.83 works — 7 works, 6 works, 0 works, −100 works. But there is a largest WHOLE number that works, and that is 7. Eight is already too big, because 6 × 8 = 48, which is past 47.

A good way to check: multiply your answer back by the coefficient and make sure it lands under the limit, then check that one more would overshoot.

One warning for later: if you ever divide an inequality by a NEGATIVE number, the sign flips direction. That does not happen here, but it is the rule that catches everyone.

Divide, then type the largest whole number that still fits.