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How do I algebraically simplify this expression #((x-5)/2-1)/3#?

Answer 1

Nathan Axel

#(x-7)/6#

#((x-5)/2-1)/3#

Find a common denominator in the numerator to simplify.

#((x-5)/2-2/2)/3#

Subtract.

#((x-7)/2)/3#

Multiply the numerator and denominator by #2#.

#(x-7)/6#

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Answer 2

Eva Adamson

To algebraically simplify the expression ((x-5)/2-1)/3, you can follow these steps:

Start by simplifying the innermost parentheses first. Subtract 1 from (x-5)/2. ((x-5)/2 - 1) becomes ((x-5)/2 - 2/2).
Combine the numerators over the common denominator. ((x-5)/2 - 2/2) becomes ((x-5-2)/2).
Simplify the numerator by combining like terms. (x-5-2) becomes (x-7).
Rewrite the expression with the simplified numerator. ((x-7)/2).
Finally, divide the entire expression by 3. ((x-7)/2) divided by 3 becomes (x-7)/6.

Therefore, the algebraically simplified expression is (x-7)/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.