An inequality is a mathematical statement that compares the values of two expressions using symbols such as <, >, ≤, or ≥. The symbol indicates whether the first expression is less than, greater than, less than or equal to, or greater than or equal to the second expression.
To solve an inequality, you need to isolate the variable (usually represented by x) on one side of the inequality sign. You can do this by using inverse operations, just like solving an equation. However, when multiplying or dividing by a negative number, you need to flip the inequality sign to maintain the correct relationship between the two expressions.
The main difference is that when solving an inequality, you have to consider the direction of the inequality sign. This is because inequalities represent a range of possible solutions, rather than just one specific solution like equations do.
Yes, you can graph an inequality on a number line or a coordinate plane. The solution to the inequality will be represented by a shaded region on the graph. If the inequality has a < or > symbol, the circle on the number line or coordinate plane representing the endpoint will be open (not filled in). If the inequality has a ≤ or ≥ symbol, the circle will be closed (filled in).
Yes, there are a few special rules to keep in mind when solving inequalities. These include: flipping the inequality sign when multiplying or dividing by a negative number, keeping track of the direction of the inequality when combining like terms, and being careful when multiplying or dividing by variables or expressions containing variables.