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How do you solve #x/(x+3)>=2#?

Answer 1

Eli Assouline

#x/(x+3)>=2#

Multiply both sides by #(x+3)#.

#x>=2(x+3)#

Apply the distributive property.

#x>=2x+6#

Subtract #2x# from both sides.

#-x>=6#

Multiply both sides by -1.

#x<=6#

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Answer 2

Hazel Anglin

To solve ( \frac{x}{x+3} \geq 2 ), first, multiply both sides by ( x+3 ) to get rid of the denominator. This gives ( x \geq 2(x+3) ). Next, expand and solve for ( x ), which yields ( x \geq 2x + 6 ). Subtract ( 2x ) from both sides to isolate ( x ), resulting in ( -x \geq 6 ). Finally, multiply both sides by ( -1 ) to make the inequality sign point the other way, giving ( x \leq -6 ). Therefore, the solution to the inequality is ( x \leq -6 ).

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Answer from HIX Tutor

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.

How do you solve #x/(x+3)&gt;=2#?

How do you solve #x/(x+3)>=2#?