1. Algebraically solve the following inequality: $5 x^{2}+18 x \geq 8$

Step 1 ：Rewrite the inequality in the standard form: \(5x^2 + 18x - 8 \geq 0\)

Step 2 ：Find the roots of the quadratic equation \(5x^2 + 18x - 8 = 0\) using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 3 ：Calculate the roots: \(a = 5, b = 18, c = -8, \text{discriminant} = 484, \text{root1} = 0.4, \text{root2} = -4.0\)

Step 4 ：Determine the intervals where the inequality is true: Since the quadratic has a positive leading coefficient (5), the parabola opens upwards. This means that the inequality will be true for values of x that are less than the smaller root or greater than the larger root.

Step 5 ：\(\boxed{x \leq -4 \text{ or } x \geq 0.4}\)