Question

Question #b8a92

Answer 1

`"see explanation"`

Explanation:

`"there is no solution to the equation"`

`x=-9" is an extraneous solution"`

`"that is a solution obtained by the simplification of the "`
`"process that does not satisfy the original equation"`

`color(blue)"As a check"`

`"left side "=3|-18+7|=3|-11|=33`

`"right side " =(3xx-9)-6=-33`

`"since left side " !=" right side"`

`rArrx=-9" is an extraneous solution"`

`"this is a valuable lesson in the need to check solutions"`

Answer 2

Because the absolute value changes the sign and positive numbers do not equal negative numbers.

Explanation:

One way to see how the `-9` is not a solution is to plug into both sides of the original

`3abs(2xx-9+7)=3xx-9-6`

`3abs(-18+7)=-27-6`

Before we go any further, you should now see these two sides cannot be equal. The left hand side will result in a positive number, but the right hand side will result in a negative number!

`3abs(-11)=-33`

Remember, absolute value makes the number inside positive.

`3xx11=-33`

`33!=-33`

If you try to solve this algebraically, you get

`3abs(2x+7)=3x-6`

Divide by `3`

`abs(2x+7)=x-6`

The trick to solving this any more depends on the sign (positive or negative) of what's inside the absolute value brackets.

If `2x+7` is a negative number, then `2x+7 < 0` which means that `2x < -7`, which means that `x < -7/2`. So for any value of `x` less than `-7/2`, the inside will become POSITIVE on the left. But plugging a number less then `-7/2` into the right side at this point will only give NEGATIVE numbers. So the expression is false for the infinite number of values less then `-7/2`.