An equation is a statement that two expressions are equal, while an inequality is a statement that two expressions are not equal, but one is greater than or less than the other.
When solving an equation, the goal is to find the value(s) of the variable that makes the equation true. The solving steps involve manipulating the equation using correct mathematical operations until the variable is isolated on one side of the equation, and the solution is obtained by simplifying the expression. The solution to an equation is generally a specific value or a finite set of values.
On the other hand, when solving an inequality, the aim is to determine the range of values for the variable that makes the inequality true. The solving steps involve manipulating the inequality similar to equation-solving steps, but with one key difference: if one performs an operation that changes the direction of the inequality symbol (e.g., multiplying/dividing by a negative number), the inequality must be reversed. The solution to an inequality is expressed as a range of values or a set of intervals that satisfy the inequality.
In summary, the main difference between an equation and an inequality lies in the solutions: an equation has a specific value or finite set of values as a solution, while an inequality has a range or set of values as a solution.
State the difference between an equation and an inequality regarding solving steps and solutions.
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