Final answer:
The inequalities are solved and visualized individually, indicating the range of values that x can take. They are also depicted on a number line. A quadratic equation is also solved, with the results checked for reasonableness within the original inequalities' context.
Step-by-step explanation:
To solve the inequalities given, we need to understand the relationships expressed by the inequality symbols. Let's start by solving and visualizing each inequality:
- x > -1.5: This means that x should be greater than minus one and a half.
- x - 6 < 0: If we add 6 to both sides, we get x < 6, indicating that x should be less than six.
- x < -0.125: Here, x should be less than negative zero point one two five.
- 0x < 0.125: Since 0 multiplied by any number is zero, this inequality simplifies to 0 < 0.125, which is always true for any value of x.
All of these inequalities can be depicted on a number line, and the solutions will be the values of x that satisfy all the inequalities simultaneously.
Now let's solve the quadratic equation x² + 1.2 x 10-2x - 6.0 × 10-3 = 0. Using the quadratic formula, we get two possible solutions for x: x = 0.0216 or x = -0.0224.