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4 January, 02:41

Solve the inequality. Write the solution set in interval notation.

2 (5 - x) ≤ 5 (x - 5)

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  1. 4 January, 03:00
    0
    x = (5,∞)

    the set of numbers from 5 to infinity

    Step-by-step explanation:

    2 (5-x) ≤5 (x-5) distribute

    10 - 2x ≤ 5x - 25 rearrange to get x's on one side, constants on the other

    10 + 25 ≤ 5x + 2x Or - 2x - 5x ≤ - 25 - 10 add like terms

    35 ≤ 7x Or - 7x ≤ - 35 if you have to divide by a negative number, flip the inequality sign! see the logic: 35/7 is 5 ≤ x - 35/-7 leaves x ≥ 5

    Either way it means 5 is less than or equal to x

    OR x is greater than or equal to 5

    in interval notation, use the infinity symbol ∞ for all numbers ≥so (5,∞)

    or - ∞ for all numbers less than.
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