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Number Systems Test - 13

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Number Systems Test - 13
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    What value of x satisfies the equation 36x − 1 = 62x − 1 − 180?

    Solution

    36x − 1 = 62x − 1 − 180 ⇒ 62(x − 1) − 62x − 1 = − 180

    ⇒ 62x − 2 − 62x − 2·6 = −180 ⇒ 62x − 2 (1 − 6) = − 180

    ⇒ − 5 × 62x − 2 = − 180 ⇒ 62x − 2 = 36

    ⇒ 62x − 2 = 62 ⇒ 2x − 2 = 2

    ⇒ 2x = 4 ⇒ x = 2

    The correct answer is D.

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