How would you solve 4 ≤ -5 -x include your steps

You want x by itself on one side of the relationship sign. You can get there a couple of ways. Here's one way.

Add 5 to both sides of the inequality.

... 4 + 5 ≤ -5 + 5 - x . . . . . 5 shown added

... 9 ≤ -x . . . . . . . . . . . . . . simplify

At this point we have -x, but we want x. If we multiply by -1, we must reverse the inequality symbol.

... -9 ≥ x . . . . . . . . . . . . . the above inequality multiplied by -1. This is the solution.

Another way to do this is to add x to the original equation. This puts it on the other side of the relationship symbol you have.

... x + 4 ≤ -5

Now, you can subtract 4 from both sides to get x by itself.

... x ≤ -9 . . . . . . . . . . the same result as above.

I like to use < or ≤ in the answer, because that puts the smaller number or expression on the left, as it is on the number line. This is not strictly necessary, but I find it convenient.

≡≡≡≡≡

With the exception of the bit about reversing the relationship symbol, inequalities are solved exactly the same way equations are solve. You "undo" each of the operations that has been done to the variable until the variable is left by itself on one side. Here, the variable was added to something, so the "undo" operation is to add the opposite of that something. When the variable is multiplied by something, the "undo" operation is to divide by that something.

As we saw, if the multiplying (or dividing) factor is negative, we must reverse the relationship symbol. You can see this if you think about negative versus positive numbers: 2 > 1 but -2 < -1.

step-by-step explanation: