Readers ask: How To Solve Absolute Value Inequalities?

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 an inequality step by step?

To solve an inequality use the following steps:

  1. Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
  2. Step 2 Simplify by combining like terms on each side of the inequality.
  3. Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

How do you do absolute value?

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines.

  1. |6| = 6 means “the absolute value of 6 is 6.”
  2. |–6| = 6 means “the absolute value of –6 is 6.”
  3. |–2 – x| means “the absolute value of the expression –2 minus x.”

What are the rules of 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.

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How do I simplify an expression?

To simplify any algebraic expression, the following are the basic rules and steps:

  1. Remove any grouping symbol such as brackets and parentheses by multiplying factors.
  2. Use the exponent rule to remove grouping if the terms are containing exponents.
  3. Combine the like terms by addition or subtraction.
  4. Combine the constants.

What is the missing step in solving the inequality 5 8x 2x 3?

Add 2x to both sides of the inequality. Subtract 8x from both sides of the inequality. Subtract 2x from both sides of the inequality.

How do you know if it’s an AND or OR inequality?

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.

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