How do you solve #abs(4x2)  6=20#?
Solve 4x  2  6 = 20
Separate solving into 2 parts:
a. (4x  2) = 26 > 4x = 28 > x = 7
b.  (4x  2) = 26 > 4x = 24 > x =  6
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To solve the equation 4x  2  6 = 20:

Add 6 to both sides of the equation to isolate the absolute value term: 4x  2 = 20 + 6 4x  2 = 26

Now, split the equation into two cases: Case 1: 4x  2 is positive Case 2: 4x  2 is negative

For Case 1 (4x  2 is positive): 4x  2 = 26 Solve for x: 4x = 26 + 2 4x = 28 x = 28/4 x = 7

For Case 2 (4x  2 is negative): (4x  2) = 26 Solve for x: 4x + 2 = 26 4x = 26  2 4x = 24 x = 24/(4) x = 6

Therefore, the solutions to the equation are x = 7 and x = 6.
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To solve the equation ( 4x  2  6 = 20 ), follow these steps:

Add 6 to both sides of the equation: ( 4x  2 = 20 + 6 = 26 )

Since the absolute value of any real number is always nonnegative, this means that ( 4x  2 ) must be equal to either 26 or 26: ( 4x  2 = 26 ) or ( 4x  2 = 26 )

Solve each equation separately: For ( 4x  2 = 26 ): ( 4x = 26 + 2 ) ( 4x = 28 ) ( x = \frac{28}{4} ) ( x = 7 )
For ( 4x  2 = 26 ): ( 4x = 26 + 2 ) ( 4x = 24 ) ( x = \frac{24}{4} ) ( x = 6 )
So, the solutions to the equation ( 4x  2  6 = 20 ) are ( x = 7 ) and ( x = 6 ).
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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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