Quick Answer: When To Use And Or Or In Absolute Value Inequalities?

How do you tell if a compound inequality is AND or OR?

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.

How do you figure out if an absolute value inequality is an AND or OR compound inequality?

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. This holds true for all absolute value inequalities. You can replace > above with ≥ and < with ≤.

Does the inequality sign change when adding or subtracting?

Adding the same number to each side of an inequality does not change the direction of the inequality symbol. If a < b, then a – c < b – c. Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.

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What does or mean when solving inequalities?

The graph of a compound inequality with an “or” represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities. It is written as x < -1 or x > 2.

How do you know if a compound inequality has no solution?

2. The solution could begin at a point on the number line and extend in one direction. 3. In cases where there is no overlap between the two inequalities, there is no solution to the compound inequality.

How do you solve and/or inequalities?

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.

How do you solve absolute value inequalities step by step?

​ Step 1:​ Isolate the absolute value expression on one side of the inequality. ​ Step 2:​ Solve the positive “version” of the inequality. ​ Step 3:​ Solve the negative “version” of the inequality by multiplying the quantity on the other side of the inequality by −1 and flipping the inequality sign.

How do you solve inequalities with absolute value?

Absolute Value Inequalities. Here are the steps to follow when solving 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.

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What are the symbols of inequalities?

These inequality symbols are: less than (<), greater than (>), less than or equal (≤), greater than or equal (≥) and the not equal symbol (≠).

What is the rule for flipping inequality signs?

Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.

What are the rules for inequalities?

When solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.

What are some real life examples of inequalities?

Situation Mathematical Inequality
Speed limit Legal speed on the highway ≤ 65 miles per hour
Credit card Monthly payment ≥ 10% of your balance in that billing cycle
Text messaging Allowable number of text messages per month ≤ 250
Travel time Time needed to walk from home to school ≥ 18 minutes

How do you solve inequalities with two variables?

To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary.

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