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12 January, 03:29

2. Find the value of x

3x + 7

+3
Answers (1)
  1. 12 January, 03:35
    0
    Answer: (x-3) / (x-7) >0

    Step-by-step explanation: Find all the values where the expression switches from negative to positive by setting each factor equal to

    0

    and solving.

    x-3=0

    x-7=0

    Add 3 to both sides of the equation.

    x = 3

    Add 7 to both sides of the equation.

    x = 7

    Solve for each factor to find the values where the absolute value expression goes from negative to positive.

    x = 3

    x = 7

    Consolidate the solutions.

    x = 3, 7

    Find the domain of x-3x-7.

    Find the domain of x - 3x-7.

    Set the denominator in

    x-3x-7

    equal to 0

    to find where the expression is undefined.

    x-7=0

    Add 7 to both sides of the equation.

    x=7

    The domain is all values of x

    that make the expression defined.

    Interval Notation:

    (-∞,7) ∪ (7,∞)

    Use each root to create test intervals.

    x< 3

    3
    >7

    Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

    x< 3 True

    3
    x>7 True

    The solution consists of all of the true intervals.

    x7

    The result can be shown in multiple forms.

    Inequality Form:

    x7

    Interval Notation:

    (-∞,3) ∪ (7,∞)
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