Solve and graph on a number line. 16. \( -13<5(1+4 m)-2 m \)

To solve the inequality \( -13 < 5(1 + 4m) - 2m \), first distribute the 5: \[ -13 < 5 + 20m - 2m \] Now combine like terms: \[ -13 < 5 + 18m \] Next, subtract 5 from both sides: \[ -18 < 18m \] Then, divide by 18: \[ -\frac{1}{1} < m \] This simplifies to: \[ m > -1 \] On a number line, you would plot an open circle at -1 (indicating that -1 is not included) with a line extending to the right, showing that m can take on any value greater than -1. Now, let’s make this learning experience even more interesting! To make things more relatable, think of it like finding the perfect seat in a theater. Here, -1 is like the front row, and you can only choose seats that are further back, meaning you're free to sit anywhere behind that front row! And if you're ever stuck on inequalities, remember to check your work. A common mistake is flipping the inequality sign when multiplying or dividing by a negative – but that’s a no-go in this case! Keep those signs straight, and you’re golden!