Question

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.

Answer 1

Answer:Ix-7I=5

Hope this helps lol

Answer 2

`|x-7|=5`

Step-by-step explanation

We know that we need to write our absolute value equation as
`|x-b|=c`. We also know that the solutions must be
`x=2` and
`x=12`. We need to replace those values for
`x` in our absolute value equation, so we can create a system of equations and find the values of
`b` and
`c`.

- For
`x=2`

`|x-b|=c`

`|2-b|=c` equation (1)

- For
`x=12`

`|x-b|=c`

`|12-b|=c` equation (2)

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

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

`|12-b|=|2-b|`

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

`|12-b|=|2-b|`

`(12-b)^2=(2-b)^2`

Step 3. Use the square of a binomial formula:
`(a-b)^2=a^2-2ab+b^2` and solve the equation.

For our first binomial,
`(12-b)^2`,
`a=12` and
`b=b`; for our second binomial,
`(2-b)^2`,
`a=2` and
`b=b`

`(12-b)^2=(2-b)^2`

`12^2-(2)(12)(b)+b^2=2^2-(2)(2)(b)+b^2`

`144-24b+b^2=4-4b+b^2`

`144-24b=4-4b`

`140=20b`

`b=(140)/(20)`

`b=7` equation (3)

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

`|12-b|=c`

`|12-5|=c`

`|7|=c`

`c=7`

Putting it all together we can conclude that our absolute value equation is
`|x-7|=5`