How do you solve #abs(2x3)<=3#?
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To solve the inequality ( 2x  3 \leq 3 ), follow these steps:

Set up two inequalities: [ 2x  3 \leq 3 ] [ (2x  3) \leq 3 ]

Solve each inequality separately: For the first inequality: [ 2x  3 \leq 3 ] Add 3 to both sides: [ 2x \leq 6 ] Divide both sides by 2: [ x \leq 3 ]
For the second inequality: [ (2x  3) \leq 3 ] Distribute the negative sign: [ 2x + 3 \leq 3 ] Subtract 3 from both sides: [ 2x \leq 0 ] Divide both sides by 2 (note that when dividing by a negative number, the inequality sign flips): [ x \geq 0 ]

Combine the solutions: The solution to the inequality ( 2x  3 \leq 3 ) is the intersection of the solutions to the two inequalities: [ 0 \leq x \leq 3 ]
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To solve the inequality ( 2x  3 \leq 3 ), you need to consider two cases: when ( 2x  3 ) is positive or zero, and when ( 2x  3 ) is negative.

When ( 2x  3 \geq 0 ): In this case, the inequality becomes ( 2x  3 \leq 3 ). Solve for ( x ): [ 2x  3 \leq 3 ] [ 2x \leq 6 ] [ x \leq 3 ]

When ( 2x  3 < 0 ): In this case, we need to consider the opposite of the expression inside the absolute value. [ (2x  3) \leq 3 ] [ 2x + 3 \leq 3 ] [ 2x \leq 0 ] [ x \geq 0 ]
So, combining both cases, the solution to the inequality ( 2x  3 \leq 3 ) is ( x \in [0, 3] ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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