Which equation would best help 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. \(4x + 5 = 2x - 9\)

Please 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.

Answered by AL2006 | 2024-06-10

The equation that best helps solve this problem is option C, which is 4x - 5 = 2x + 9. By combining the expressions for 'Five added to 4 times a number' and '9 less than 2 times the number', we can solve for x and find that x equals -7. ;

Answered by AliciaAugello | 2024-06-18

The best equation to help solve the problem is option D: 4 x + 5 = 2 x − 9 . This equation accurately represents "five added to 4 times a number is equal to 9 less than 2 times the number." Each part of the problem statement is translated correctly into mathematical terms.
;

Answered by AL2006 | 2024-10-14