Final answer:
To solve the inequality 5x² + 7x -2, we need to rewrite it in the form ax² + bx + c < 0. The solution to the inequality is x < -7/5 or x > 0.
Step-by-step explanation:
To solve the inequality 5x² + 7x -2, we need to rewrite it in the form ax² + bx + c < 0. Let's first rewrite the inequality as the quadratic expression (5x² + 7x) / (x²).
Next, we can factor out the common factors and simplify the expression to (5x + 7) / x² < 0. Now, we need to consider the intervals where the expression is negative.
By applying the sign test method, we can determine that the solution to the inequality is x < -7/5 or x > 0. As a result, the solution to the inequality is (-∞, -7/5) U (0, +∞).