How To Solve Absolute Value Equations With A Number On The Outside?

How do you solve an absolute value equation step by step?


  1. Step 1: Isolate the absolute value expression.
  2. Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
  3. Step 3: Solve for the unknown in both equations.
  4. Step 4: Check your answer analytically or graphically.

What happens when you add a number outside of the absolute value bars?

The absolute value of a negative number makes it a positive number. Placing absolute value bars around 0 doesn’t change its value, so |0| = 0. Placing a minus sign outside absolute value bars gives you a negative result — for example, –|6| = –6, and –|–6| = –6.

What are the 3 major steps to solving an absolute value equation?

We will be using the following 3 – step process that can be used to solve any absolute value equation:

  • STEP ONE: Isolate the Absolute Value.
  • STEP TWO: Solve for Positive AND Solve for Negative.
  • STEP THREE: Check Your Answer.
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What are the major points for solving an absolute value equation?

Key Point #2: The x inside the absolute value symbol, ∣ ∣ left| {,,,,,} right| ∣∣, could be any expressions. Key Point #3: The a on the right side of the equation must be either a positive number or zero to have a solution. Key Point #4: If the a on the right side is a negative number, then it has no solution.

How do you solve absolute value inequalities?

You begin by making it into two separate equations and then solving them separately. 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.

How do you solve absolute value equations and inequalities?

Key Takeaways

  1. To solve an absolute value equation, such as |X|=p, replace it with the two equations X=−p and X=p.
  2. To solve an absolute value inequality involving “less than,” such as |X|≤p, replace it with the compound inequality −p≤X≤p and then solve as usual.

What are the rules of absolute value?

Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number’s sign: if it’s positive, it’s equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.

Is absolute value the same as parentheses?

Sometimes parentheses are added to organize and group the same kinds of things. Absolute value signs make the final result of the operations between them positive. When deciding on the order of operations, treat absolute value bars like parentheses.

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What is the absolute value of 3?

For example, the absolute value of 3 is 3, and the absolute value of − 3 is also 3. The absolute value of a number may be thought of as its distance from zero.

How do you know if an absolute value inequality is no solution?

Here are the steps to follow when solving absolute value inequalities:

  1. Isolate the absolute value expression on the left side of the inequality.
  2. 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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