Choose the missing a step in the given solution to the inequality : -x- 10 > 14 +2x
-x - 10 > 14 +2x
-3x - 10 > 14

x< -8
answer choices: a: -3x> 24 b: -3x> 4 c: -3x> -4 d: -3x< 24

  A:  -3x > 24

Step-by-step explanation:

The missing step above is the result of adding 10 to both sides of the inequality.

Comment on the solution of this inequality

The solution shown is correct and gives correct results, but it requires that you divide by a negative number. That division can be by a positive number if the first step is to add x to both sides. Then the second step is to subtract 14 and you get ...

  -24 > 3x

Division by a negative number is not required, and the direction of the inequality stays the same:

  -8 > x

Further comment on the solution

Using left-pointing inequality symbols (< or ≤) arranges the left-right order of the operands the same way they are arranged on the number line. That is, for the solution to this inequality, all of the values of x are to the left of -8 on the number line. Writing the inequality in the form ...

  x < -8

can help you see that. A bit of mental gymnastics is required when the inequality is written ...

  -8 > x

and you want to graph or choose values of x that match this result. Of course, once you have -8>x, you can easily swap sides to make it x<-8.