Question

(Sorry its math not geography,,,)

Savannah solve the equation 3 + 4|x/2 + 3| = 11 for one solution. Her work is shown below:

1. 4|x/2 + 3| = 8

2. |x/2 + 3| = 2

3. x/2 + 3 = 2

4. x/2 = -1

5. x = -2

What is the other solution to the given absolute value equation?​

Answer 1

Problem:
`4|(x)/(2)+3|=8`.

Solution given:
`x=-2`

The other solution:
`x=-10`

Step-by-step explanation:

`|(x)/(2)+3|=2`

Means the value inside the absolute value has to be 2 or -2 since |2|=2 and |-2|=2.

So you already have
`(x)/(2)+3=2`.

You need that
`(x)/(2)+3=-2`.

Let's solve this equation:

`(x)/(2)+3=-2`

Subtract 3 on both sides:

`(x)/(2)=-2-3`

Simplify:

`(x)/(2)=-5`

Multiply both sides by 2:

`x=-5(2)`

Simplify:

`x=-10`

So x=-2 or x=-10.

Checking!

x=-2:

`4|(-2)/(2)+3|=8`

`4|-1+3|=8`

`4|2|=8`

`4(2)=8`

`8=8` is true so x=-2 checks out.

x=-10:

`4|(-10)/(2)+3|=8`

`4|-5+3|=8`

`4|-2|=8`

`4(2)=8`

`8=8` is true x=-10 checks out.

It has been confirmed that -2 and -10 satisfy the equation:

`4|(x)/(2)+3|=8`.