how do you solve an inequality and graph it's solution?
To solve an inequality and graph its solution, follow these steps:
1. First, treat the inequality like an equation and solve for the variable. However, remember that if you multiply or divide by a negative number, you need to reverse the inequality symbol.
For example, let's say we have the inequality: 2x + 3 < 5. We can solve it by subtracting 3 from both sides: 2x < 2. Then, divide both sides by 2 to isolate x: x < 1.
2. After solving for the variable, graph the solution on a number line. Start by plotting any critical points, such as the equal sign or any breaks in the number line caused by the inequality. In this case, x = 1 is a critical point.
3. Based on the inequality symbol (<, >, ≤, ≥), determine whether the critical point is included in the solution or not. If the symbol is "<" or ">", it means the point is not included. If the symbol is "≤" or "≥," it means the point is included.
4. If the symbol is "<" or "≤", shade the number line to the left of the critical point. If the symbol is ">" or "≥", shade the number line to the right of the critical point. The shaded region represents the solution to the inequality.
To summarize, the steps to solve and graph an inequality are:
1. Solve the inequality by isolating the variable, reversing the inequality sign if necessary.
2. Plot critical points on a number line.
3. Determine if the critical point is included in the solution or not based on the inequality symbol.
4. Shade the appropriate region on the number line to represent the solution.
Remember, graphing inequalities may vary slightly depending on the context and the specific inequality given.