Problem 122 - College Algebra

Question

Solve each inequality using a graphing utility. Graph each side separately. Then determine the values of \(x\) for which the graph on the left side lies above the graph on the right side. $$-2(x+4)>6 x+16$$

Step-by-Step Solution

Answer

The exact solution will depend on how the functions are graphed and may need verification. This is a visual approach, and the solution lies in the interval of x-values where the graph of \( y1 = -2(x+4) \) is above the graph of \( y2 = 6x+16 \).

Step 1: Rewrite

Rewrite the inequality \( -2(x+4)>6x+16 \) into two equations to visually graph them. They are \( y1 = -2(x+4) \) and \( y2 = 6x+16 \)

Step 2: Graph Equations

Plot the functions \( y1 = -2(x+4) \) and \( y2 = 6x+16 \) on a graphing utility. It is important to see the parts of two graphs in relation to each other.

Step 3: Determine Solution

The solution to the inequality is the interval of x-values where the graph of \( y1 = -2(x+4) \) lies above the graph of \( y2 = 6x+16 \). Carefully observe where the first function is higher than the second function to find the interval of solution.