# How Can You Use Linear Equations To Solve An Absolute Value Equation Big Ideas Math? (Solution found)

• Collaborate with a colleague. Take, for example, the absolute value equation x+2=3. Explanation: Give examples of the values of x +2 that result in the equation being true. Take the information from your description and build two linear equations that represent two solutions to the absolute value equation. Calculate all possible solutions to the absolute value equation by using the linear equations that you wrote in step (a).

## How can you use linear equations to solve an absolute value equation?

Isolate the absolute value on one side of an equation to solve an equation involving absolute value. Set the contents of the array equal to both the positive and negative values of the integer on the opposite side of the equation and answer both equations simultaneously.

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

We will be employing the three-step procedure outlined below, which may be used to the solution of any absolute value equation:

• FIRST, isolate the absolute value.
• SECOND, solve for both the positive and negative values.
• FIRST, isolate the absolute value.

## Can you have absolute value in a linear equation?

Because any numbers may be entered into an absolute value or linear equation, the domains of both absolute value and linear equation encompass all real numbers. Due to the fact that absolute values cannot be negative, the minimum conceivable value for them is 0. Linear equations, on the other hand, may describe values that are either negative, zero, or positive.

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## What’s an absolute value equation?

When a variable is included within an absolute value operator, such as |x-5|=9, it is referred to as an absolute value equation. If the number is negative, the absolute value is equal to the number’s inverse: |-9|=9. As a result, while dealing with a variable, we must take into account both possibilities.

## How do you solve absolute value equations with notes?

To Solve Absolute Value Equations, follow these steps:

1. Separate the absolute value expression from the rest of the expression on one side of the equal sign. Create a new absolute value by setting the interior of the absolute value equal to + and – values on the other side of the equal sign (do not include the absolute value bars in this step). If necessary, find the variable in these two new equations and solve for it.

## Do absolute value equations always have two solutions?

Whenever you encounter an absolute value equation, you will always follow the same procedure: first, isolate the absolute value term, and then build equations that are based on the definition of the absolute value. It is possible that there will be two solutions, one solution, or no solutions.