Question
4(x+ 2) β₯2x-2 find the range of x
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Answer to a math question 4(x+ 2) β₯2x-2 find the range of x
Corbin
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To find the range of x that satisfies the inequality 4(x + 2) β₯ 2x - 2, we can solve it step by step. Let's begin:
4(x + 2) β₯ 2x - 2
First, distribute 4 to both terms inside the parentheses:
4x + 8 β₯ 2x - 2
Next, let's isolate the terms with x on one side of the inequality by subtracting 2x from both sides:
4x - 2x + 8 β₯ -2
Simplifying the left side:
2x + 8 β₯ -2
Now, let's isolate the term with x by subtracting 8 from both sides:
2x + 8 - 8 β₯ -2 - 8
Simplifying both sides:
2x β₯ -10
Finally, to solve for x, we divide both sides by 2. Since we are dividing by a positive number, the direction of the inequality remains the same:
(2x)/2 β₯ (-10)/2
x β₯ -5
Therefore, the range of x that satisfies the inequality 4(x + 2) β₯ 2x - 2 is x β₯ -5.
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