Problem 86 - Algebra and Trigonometry

Question

Solve each inequality in Exercises \(86-91\) using a graphing utility. $$ x^{2}+3 x-10>0 $$

Step-by-Step Solution

Answer

The solution to the given inequality \(x^{2}+3 x-10>0\) would depend on the roots of the related equation, which you can solve for to find the respective intervals for x that satisfy the inequality.

Step 1: Graph the Related Equation

Input the related equation \(x^{2}+3 x-10=0\) into a graphing utility. Look for the points where the graph intersects the x-axis, those are the solutions to the equation and will serve as your critical numbers.

Step 2: Find the X-Intercepts (Roots)

Identify the x-values of the x-intercepts. These will be the roots or solutions of the equation. Solve \(x^{2}+3x-10=0\) to find these values.

Step 3: Test the Intervals

Select test points from intervals determined by the x-intercepts. Substitute these test points into the inequality. If the inequality holds true, include that interval in the solution set. If it is false, exclude that interval.

Step 4: Write the Solution

Write the solution as an inequality or in interval notation using the information from the intervals that satisfied the inequality.