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Algebra 1

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Solve each equation. Rewrite the equation as two cases.

1). The absolute value of x - 2 minus 3 equals 5.

A: I know one of the solutions is 10. However, I do not believe there is a second solution.

2). The absolute value of x + 7 increased by 2 = 10.

A: I know one of the solutions is 1. However, I am uncertain of what the other is.

  • Algebra 1 - ,

    1 )

    | x - 2 | - 3 = 5 Add 3 to both sides

    | x - 2 | - 3 + 3 = 5 + 3

    | x - 2 | = 8

    x - 2 = + OR - 8


    First solution :

    x - 2 = 8 Add 2 to both sides

    x - 2 + 2 = 8 + 2

    x = 10

    Second solution :

    x - 2 = - 8 Add 2 to both sides

    x - 2 + 2 = - 8 + 2

    x = - 6


    Solutions :

    x = - 6 and x = 10


    2 )

    | x + 7 | + 2 = 10 Subtract 2 to both sides

    | x + 7 | + 2 - 2 = 10 - 2

    | x + 7 | = 8

    x + 7 = + OR - 8


    First solution :

    x + 7 = 8 Subtract 7 to both sides

    x + 7 - 7 = 8 - 7

    x = 1

    Second solution :

    x + 7 = - 8 Subtract 7 to both sides

    x + 7 - 7 = - 8 - 7

    x = - 15


    Solutions :

    x = 1 and x = - 15

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