Write the absolute value equation if it has the following solutions. hint: your equation should be written as |x−b| =c. (here b and c are some numbers.) chapter reference b two solutions: x=2, x=12.

We know that we need to write our absolute value equation as . We also know that the solutions must be and . We need to replace those values for in our absolute value equation, so we can create a system of equations and find the values of   and .

- For

equation (1)

- For

equation (2)

Now we can solve our system of equations step-by-step:

Step 1. Replace equation (1) in equation (2)

Step 2. Square both sides of the equation to get rid of the absolute values

Step 3. Use the square of a binomial formula: and solve the equation.

For our first binomial, , and ; for our second binomial, , and

equation (3)

Step 4. Replace equation (3) in equation (2) to find the value of

Putting it all together we can conclude that our absolute value equation is

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step-by-step explanation: