Which equation would best solve this problem?
five added to 4 times a number is equal to 9 less than 2 times the number.
a.9x + 2 = 5x + 4
b.5x + 4 = 9x – 2
c.4x – 5 = 2x + 9
d.4x + 5 = 2x – 9
explain the answer : )

Just give the unknown number a name ... like 'Q' ... and then take the description phrase by phrase, one at a time:

"Five" . . . that one is pretty easy.

"4 times a number" . . . 4Q

"Five added to 4 times a number" . . .    5 + 4Q

"2 times the number" . . .   2Q

"9 less than 2 times the number" . . .    2Q - 9

The first quantity is equal to the second quantity . . .     5 + 4Q  =  2Q - 9

That's choice D.

What if you had to solve it, and find the mysterious unknown number.
Could you handle it from here ?

5 + 4Q  =  2Q - 9

Subtract  5  from each side:          4Q  =  2Q - 14

Subtract  2Q  from each side:          2Q  =  -14

Divide each side by  2 :                    Q  =  -7

-7  is the only number that will make that original long messy statement true.

 

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