solve for n.\n1.94 + 5(1.92n + 1.84) = 0.3(22n - 6.2) - 2\nn =

Explanation:

Step1: Expand both sides

Expand (5(1.92n + 1.84)) using distributive property (a(b + c)=ab+ac): (5\times1.92n+5\times1.84 = 9.6n+9.2). Expand (0.3(22n - 6.2)) using distributive property: (0.3\times22n-0.3\times6.2=6.6n - 1.86). The equation becomes (1.94+9.6n + 9.2=6.6n-1.86 - 2).

Step2: Simplify both sides

Simplify the left - hand side: (1.94 + 9.2+9.6n=11.14+9.6n). Simplify the right - hand side: (6.6n-(1.86 + 2)=6.6n-3.86). The equation is now (11.14+9.6n=6.6n-3.86).

Step3: Move terms with (n) to one side

Subtract (6.6n) from both sides: (11.14+9.6n-6.6n=6.6n-6.6n - 3.86). (11.14 + 3n=-3.86).

Step4: Isolate the term with (n)

Subtract (11.14) from both sides: (3n=-3.86-11.14). (3n=-15).

Step5: Solve for (n)

Divide both sides by (3): (n=\frac{-15}{3}).

Answer:

(n=-5)