Solve for x.

one seventh times the absolute value of the quantity x minus 3 end quantity minus 2 equals 9

x = 74 and x = 80
x = −46 and x = 52
x = −52 and x = 46
x = −74 and x = 80

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facundo3141592 facundo3141592 · Answer 1 · 2022-08-12T18:18:09+02:00

The solutions to the given absolute value equation are:

x = −74 and x = 80

Here we want to solve the absolute value equation:

(1/7)*|x - 3| - 2 = 9

To solve this, we first need to isolate the absolute value part, so we get:

(1/7)*|x - 3| - 2 = 9

(1/7)*|x - 3| = 9 + 2

(1/7)*|x - 3| = 11

|x - 3| = 11*7

|x - 3| = 77

Now we can decompose the absolute value equation into two simpler ones, which are:

x - 3 = 77

x - 3 = -77

Solving those two equations we get:

x = 77 + 3 = 80

x = -77 + 3 = -74

Thus the solutions are:

x = -74 and x = 80, we conclude that the correct option is the last one.

If you want to learn more about absolute value equations:

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