Why do you flip the inequality sign?
Much like when you divide by a negative number, the sign of the inequality must flip! Here’s why: When you multiply both sides by a negative value you make the side that is greater have a “bigger” negative number, which actually means it is now less than the other side!
When should you flip the inequality?
Flip the inequality sign when you multiply or divide both sides of an inequality by a negative number. You also often need to flip the inequality sign when solving inequalities with absolute values.
Do you flip the inequality sign when subtracting?
Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol. If a < b and if c is a positive number, then a · c < b · c. Multiplying each side of an inequality by a positive number does not change the direction of the inequality symbol.
What are the rules of inequalities?
If you add the same number to both sides of an inequality, the inequality remains true. If you subtract the same number from both sides of the inequality, the inequality remains true. If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.
What are the four inequality symbols?
These inequality symbols are: less than (<), greater than (>), less than or equal (≤), greater than or equal (≥) and the not equal symbol (≠).
What happens to inequalities when you divide?
Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged. Rule 3. Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa.
How do you solve absolute value inequalities?
Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds.
Does the inequality sign change when taking square root?
Taking a square root will not change the inequality (but only when both a and b are greater than or equal to zero).
How did you find the solution set of each inequality?
You will determine the solution set of an inequality by equating them first into zero. After that try to substitute the value of X. Then after, you will find out the right sign that you will use.
How do you know if inequality is AND or OR?
A compound inequality is just more than one inequality that we want to solve at the same time. We can either use the word ‘and’ or ‘or’ to indicate if we are looking at the solution to both inequalities (and), or if we are looking at the solution to either one of the inequalities (or).
How do you simplify an inequality?
Summary. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.
How do you solve and inequality?
To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be a union of sets (“or”) or an intersection of sets (“and”). Then, solve both inequalities and graph.