Math  /  Algebra

QuestionSolve the compound inequality: x+4>8x+4>8 or 4x>64-x>6. Provide the solution set in interval and graph forms.

Studdy Solution
For the graph, we plot two rays on a number line. The ray for x>4x >4 starts at4 and goes to the right (towards positive infinity). The ray for x<2x < -2 starts at -2 and goes to the left (towards negative infinity). Both rays are open at their starting points (4 and -2) because the inequalities are strict (i.e., xx can't be equal to4 or -2).
The solution set for the compound inequality x+4>8x+4>8 or 4x>64-x>6 is (4,)(4, \infty) or (,2)(-\infty, -2).

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