Question

A number decreased by the sum of the number and eight.

What is the algebraic expression?
(Do not simplify)

Answer 1

Hi!

I can help you with joy! :)

First of all, "the sum of" means we add.

Let the number be r.

So, we add r and 8:

r+8

Now, "decreased" means we subtract, so we subtract

r-(r+8) (Final Answer)

Simplified Form:

r-(r+8)

r-r+8

`\fbox{8}\checkmark`

Hope it helps!

Enjoy your day!

Feel free to ask if you have any doubts.

~Misty~

Answer 2

The answer is: " x – (x + 8) " .

{Note: The simplified form is: " -8 ."}.
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Explanation:
We are given:

→ " A number decreased by the sum of the number and eight."
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Let "x" represent the number referred to as "a number."

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"{A number} decreased by {the sum of the (number and eight).}" ;

↑ ↑ ↑

"x" "(minus)" " (x + 8) " ;
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So; we can write this as:
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→ " x – (x + 8) " ;
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Edit—Addendum:

{Now, if are then asked to simply this expression}:
→ " x – (x + 8) " ;
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Then: Rewrite as:
→ " x – 1(x + 8) " ;
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Take note of the distributive property of multiplication:
→ " a(b + c) = ab + ac " ;

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Likewise:
→ " x – 1(x + 8) " ;

→ Note the: " -1(x + 8) ";
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→ -1(x + 8) = (-1*x) + (-1*8) ;

= (-1x) + (-8) ;
= (-1x – 8) ;
Now, bring down the " ⁺x " :
→ " x – 1x – 8 " ;
Rewrite as:
→ " 1x – 1x – 8 " ;
Simplify:
→ " 1x – 1x – 8 " ;

= " (1x – 1x) – 8 " ;

= " (0 – 8) " ;

= " -8 " ; which is the simplified form of the
given algebraic expression.
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Hope this explanation is helpful to you!
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