Question

-43 times the difference between a number and 74 is equal to the number plus - 64.​

Answer 1

Answer: -43( n - 74) = n + (-64)

Step-by-step explanation:

The statement can be represented by the equation

-43( n - 74) = n + (-64)  where n is the number

Answer 2

Answer:

$\huge\boxed{-43(n-74)=n+(-64)}\\\boxed{n=\dfrac{1623}{22}=73\dfrac{17}{22}}$

Step-by-step explanation:

$n-\text{a number}\\\\\text{the difference between a number and 74}:\ n-74\\\\\text{-43 times the difference between a number and 74}:\ -43(n-74)\\\\\text{the number plus - 64:}\ n+(-64)\\\\\text{The equation}:\\\\-43(n-74)=n+(-64)$

$solution$

$-43(n-74)=n+(-64)\qquad/\text{use the distributive property}\\\\(-43)(n)+(-43)(-74)=n-64\\\\-43n+3182=n-64\qquad/\text{subtract 3182 from both sides}\\\\-43n=n-3246\qquad/\text{subtract}\ n\ \text{from both sides}\\\\-44n=-3246\qquad/\text{divide both sides by (-44)}\\\\n=\dfrac{-3246}{-44}\\\\n=\dfrac{3246:2}{44:2}\\\\\boxed{n=\dfrac{1623}{22}=73\dfrac{17}{22}}$