# Let #f(x)= 3- (x+ 4)+ 2x#. How do you find all values of x for which f(x) is at least 6?

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Solution:

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To find all values of x for which ( f(x) ) is at least 6, you solve the inequality ( f(x) \geq 6 ).

( f(x) = 3 - (x + 4) + 2x )

First, simplify the function:

( f(x) = 3 - x - 4 + 2x ) ( f(x) = -x - 1 + 2x ) ( f(x) = x - 1 )

Now, solve the inequality:

( x - 1 \geq 6 )

Add 1 to both sides:

( x \geq 7 )

So, all values of x for which ( f(x) ) is at least 6 are ( x \geq 7 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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