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How do you use the distributive property to simplify #-(12-4x)+8(10-x)#?

Answer 1

The simplified form is #-4x+68#

The Distributive Property is when you apply a coefficient to all terms inside a set of parentheses. For this expression, we will use The Distributive Property twice:

#-(12-4x)+8(10-x)=-1xx(12-4x)+8xx(10-x)#

Let's do the first distribution:

#-1xx(12-4x)=(-1xx12)-(-1xx4x) = (-12)-(-4x)#

#rArr-12+4x#

...And now the second:

#8xx(10-x)=(8xx10)-(8xx x) = (80)-(8x)#

#rArr80-8x#

Finally, we put these two distributed expressions back into the original equation and simplify:

#-12+4x+80-8x = 4x-8x+80-12#

#color(red)(rArr -4x+68)#

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Answer 2

Eli Assouline

To simplify -(12-4x) + 8(10-x) using the distributive property:

Distribute the negative sign and the 8: -(-(12-4x)) + 8(10) - 8(-x)
Simplify each term: -(-12 + 4x) + 80 - 8x
Remove the double negative: 12 - 4x + 80 - 8x
Combine like terms: 12 + 80 - 4x - 8x
Simplify further: 92 - 12x

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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.