How do you solve #|x-5|+|2-2x|=7 #?
The roots are
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To solve the equation ( |x-5| + |2-2x| = 7 ):
- Split the equation into cases based on the possible values inside the absolute value expressions.
- Solve each case separately.
- Check if the solutions obtained are valid by substituting them back into the original equation.
The possible cases are:
- ( x - 5 \geq 0 ) and ( 2 - 2x \geq 0 )
- ( x - 5 \geq 0 ) and ( 2 - 2x < 0 )
- ( x - 5 < 0 ) and ( 2 - 2x \geq 0 )
- ( x - 5 < 0 ) and ( 2 - 2x < 0 )
Solve each case separately and then check the solutions obtained to ensure they satisfy the original equation.
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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.
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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