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12 December, 00:23

Solve for |2x + 4|-1=7

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  1. 12 December, 00:41
    0
    x = - 6 or x = 2

    Step-by-step explanation:

    The absolute value function always returns a positive value. However, the expression inside can be positive or negative.

    Given

    | 2x + 4 | - 1 = 7 (add 1 to both sides)

    | 2x + 4 | = 8, thus

    2x + 4 = 8 (subtract 4 from both sides)

    2x = 4 (divide both sides by 2)

    x = 2

    OR

    - (2x + 4) = 8

    - 2x - 4 = 8 (add 4 to both sides)

    - 2x = 12 (divide both sides by - 2)

    x = - 6

    As a check

    Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

    x = 2 → | 4 + 4 | - 1 = | 8 | - 1 = 8 - 1 = 7 ← True

    x = - 6 → | - 12 + 4 | - 1 = | - 8 | - 1 = 8 - 1 = 7 ← True

    Hence the solutions are x = - 6 or x = 2
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