Question #b8a92

2 Answers
Jun 22, 2017

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

As a check

left side =3|18+7|=3|11|=33

right side =(3×9)6=33

since left side right side

x=9 is an extraneous solution

this is a valuable lesson in the need to check solutions

Jun 22, 2017

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

3|2×9+7|=3×96

3|18+7|=276

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!

3|11|=33

Remember, absolute value makes the number inside positive.

3×11=33

3333

If you try to solve this algebraically, you get

3|2x+7|=3x6

Divide by 3

|2x+7|=x6

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<72. So for any value of x less than 72, the inside will become POSITIVE on the left. But plugging a number less then 72 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 72.