Question

Please help! 7|-7x-3|=21

Answer 1

Divide by 7.

... |-7x -3| = 3

Unfold to two equations.

... -3 = -7x -3 . . . . . the content of the absolute value is negative

... 0 = -7x . . . . . . . . add 3

... 0 = x . . . . . . . . . . divide by -7

and

... 3 = -7x -3 . . . . . . the content of the absolute value is positive

... 6 = -7x . . . . . . . . add 3

... -6/7 = x . . . . . . . . divide by -7

The solutions are ...

... x = -6/7 or x = 0

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Many graphing programs will happily tell you the locations of x- and y-intercepts, so it is convenient to rewrite the equation so its value is zero at the solution points. We can do that by subtracting the right side constant to get ...

... 7|-7x -3| -21 = 0