Question

question 3 of 8
select the correct answer.
consider the equation below.
boxed equation, likely linear in n
select the equation that has the same solution.
-1 - 12n = -20n - 9
1 = 0.75n + 3.25
3 - 8n + 9n = -3 + 4 - 4n
\\(\frac{3}{4}n + 3 = -5 + \frac{7}{4}n\\)

Explanation:

Step1: Solve the original equation

First, solve $3n - 1 = 4n - 3$:
Subtract $3n$ from both sides:
$-1 = n - 3$
Add 3 to both sides:
$n = 2$

Step2: Test Option 1

Solve $-1 - 33n = -30n - 9$:
Bring like terms together:
$-33n + 30n = -9 + 1$
$-3n = -8$
$n = \frac{8}{3}
eq 2$

Step3: Test Option 2

Solve $1 = 0.75n + 3.25$:
Subtract 3.25 from both sides:
$1 - 3.25 = 0.75n$
$-2.25 = 0.75n$
$n = \frac{-2.25}{0.75} = -3
eq 2$

Step4: Test Option 3

Solve $3 - 6n + 3n = -3 + 4 - 4n$:
Simplify both sides:
$3 - 3n = 1 - 4n$
Bring like terms together:
$-3n + 4n = 1 - 3$
$n = -2
eq 2$

Step5: Test Option 4

Solve $\frac{3}{4}n + 3 = -3 + \frac{9}{4}n$:
Bring like terms together:
$3 + 3 = \frac{9}{4}n - \frac{3}{4}n$
$6 = \frac{6}{4}n$
$6 = \frac{3}{2}n$
$n = 6 \times \frac{2}{3} = 2$

Answer:

$\frac{3}{4}n + 3 = -3 + \frac{9}{4}n$