To solve an inequality with variables on both sides, you need to isolate the variable on one side of the inequality sign. You can do this by using inverse operations, such as adding or subtracting the same number from both sides, or multiplying or dividing both sides by the same number. Once the variable is isolated, you can solve for its value.
The main difference between solving an inequality and solving an equation is that inequalities have a range of solutions, while equations have a single solution. Inequalities also use inequality symbols (<, >, ≤, ≥) instead of an equal sign (=).
Yes, you can graph an inequality by first solving it and then plotting the solutions on a number line. The solutions will be shaded to indicate the range of values that satisfy the inequality. If the inequality is strict (>, <), the endpoint will be an open circle, while if it is inclusive (≥, ≤), the endpoint will be a closed circle.
The type of inequality symbol used in the problem will determine if the solution is inclusive or exclusive. If the symbol is ≤ or ≥, the solution will be inclusive, meaning the endpoint is included in the solution. If the symbol is < or >, the solution will be exclusive, meaning the endpoint is not included in the solution.
Yes, you can check your solution to an inequality by plugging it back into the original inequality. If the solution makes the inequality true, then it is a valid solution. If it makes the inequality false, then it is not a valid solution. You can also graph the solution and see if it falls within the shaded region on the number line.