Final answer:
To solve the inequality −1 < 2x, divide each side by 2 to get x > −½. The solution is graphed on a number line with an open circle on −½ and shading to the right. Further details addressing unrelated quadratic equations were provided for context.
Step-by-step explanation:
To solve for x and graph the solution on a number line, we have the inequality −1 < 2x, which we need to rearrange into the form x > −½ to isolate x on one side. By dividing each side by 2, we get x > −½. To graph this on the number line, make an open circle on −½ and shade to the right, indicating that x is any number greater than −½.
The information given about using the quadratic equation to find x is unrelated to the inequality we are solving. However, when solving a quadratic equation, we often get two solutions. We use x = −b ± √(b² − 4ac) / 2a to find these solutions. After checking for real-life applicability or the context in which the problem is given, some solutions may not be valid, and we might need to discard the unrealistic ones.