Question

Choose the missing step in the given solution to the inequality −x − 3 < 13 + 3x.

−x − 3 < 13 + 3x
___________
−4x < 16
x > −4

Answer 1

To find the missing step in the given solution, let's work through the inequality:

−x − 3 < 13 + 3x

To isolate the variable x, we can start by adding x to both sides:

−x + x − 3 < 13 + 3x + x

Simplifying:

−3 < 13 + 4x

Next, we subtract 13 from both sides:

−3 − 13 < 13 + 4x − 13

Simplifying:

−16 < 4x

Now, we need to divide both sides by 4. However, we must remember to reverse the inequality sign when dividing by a negative number:

−16/4 > 4x/4

Simplifying:

−4 > x

The correct missing step is x < -4.