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    Which of the following is the solution of the given inequality,8x + 2 ≥ 2x + 14, where x is a real number?
    Question

    Which of the following is the solution of the given inequality,

    8x + 2 ≥ 2x + 14, where x is a real number?

    A.

    (―∞, ∞)

    B.

    [-2, 2]

    C.

    [2, ∞)

    D.

    (2, ∞)

    Correct option is C

    8x+22x+14Subtract 2x from both sides:6x+214Subtract 2 from both sides:6x12Divide both sides by 6:x2\begin{aligned}&8x + 2 \geq 2x + 14 \\[10pt]&\text{Subtract } 2x \text{ from both sides:} \\&6x + 2 \geq 14 \\[10pt]&\text{Subtract 2 from both sides:} \\&6x \geq 12 \\[10pt]&\text{Divide both sides by 6:} \\&x \geq 2\end{aligned}

    \therefore solution can be written as [2,\infin).​

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