Question

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

Answers

  1. The solutions to the given absolute value equation are:
    x = −74 and x = 80

    How to solve the given equation for x?

    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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