Question

solve the inequality.
3w - 5 > 2w + w - 7
○ w > -2
○ all real numbers
○ no solution
○ w < -2

which of the following graphs represents the solution?
graph options with number lines (e.g., arrows, -3 to 3, open/closed circles)

Explanation:

Step1: Simplify both sides

Simplify the right - hand side of the inequality \(3w - 5>2w + w-7\). Combine like terms on the right: \(2w+w = 3w\), so the inequality becomes \(3w - 5>3w-7\).

Step2: Subtract \(3w\) from both sides

Subtract \(3w\) from each side of the inequality: \((3w - 5)-3w>(3w - 7)-3w\). This simplifies to \(- 5>-7\).

Since \(-5\) is always greater than \(-7\) for any real number \(w\) (because the \(w\) terms canceled out and we are left with a true statement about constants), the solution to the inequality is all real numbers.

For the graph of the solution (all real numbers), the graph should be a number line with an arrow pointing in both directions (or a line that covers the entire number line). Among the given graphs, the one that represents all real numbers is the one with no breaks and arrows in both directions (the second graph option with the line covering from \(-3\) to \(3\) and beyond in both directions).

Answer:

The solution to the inequality \(3w - 5>2w + w-7\) is "All real numbers", and the graph that represents all real numbers is the one with the line spanning the entire number line (the second graph option in the list of graph choices).