When solving an equation, the goal is to find the value(s) that satisfy the equation and make it true. Equations are primarily concerned with equality.
On the other hand, when solving an inequality, the goal is to find the range of values that satisfy the inequality. Inequalities involve a comparison of values, typically using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
The main difference to keep in mind when solving an inequality is how the solution is affected when performing operations on both sides of the inequality sign. There are three crucial aspects to consider:
1. Multiplication or Division by a negative number: If an inequality is multiplied or divided by a negative number, the direction of the inequality must be reversed. For example, if you have the inequality 2x > 6 and you multiply both sides by -1, you need to change the inequality sign to obtain -2x < -6.
2. Addition or Subtraction by a negative number: Adding or subtracting a negative number is equivalent to adding or subtracting the positive number of the same value. No changes are required to the direction of the inequality. For example, if you have the inequality x + 3 < 7 and you subtract 3 from both sides, you have x < 4.
3. Multiplication or Division by a positive number: When multiplying or dividing an inequality by a positive number, there is no need to change the direction of the inequality. For example, if you have the inequality 3x < 9 and you divide both sides by 3, you have x < 3.
It is important to note that when solving inequalities, the solution can often be expressed in different forms, such as interval notation or set notation, depending on the context and requirements of the problem.
what is the main difference you have to keep in mind when solving an equation v. an inequality?
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