Question

question 3 of 8
select the correct answer.
consider the equation below.
-5n + 31 = -14n - 5
select the equation that has the same solution.
-1 - 22n = -20n - 9
1 = 0.75n + 3.25
3 - 6n + 3n = -3 + 4 - 4n
\\(\frac{11}{4}n + 2 = -3 + \frac{3}{2}n\\)

Explanation:

Step1: Solve the original equation

Start with $-5n + 31 = -14n - 5$.
Add $14n$ to both sides:
$-5n + 14n + 31 = -5$
$9n + 31 = -5$
Subtract 31 from both sides:
$9n = -5 - 31$
$9n = -36$
Divide by 9:
$n = \frac{-36}{9} = -4$

Step2: Test Option 1

Solve $-1 - 22n = -20n - 9$.
Add $22n$ to both sides:
$-1 = 2n - 9$
Add 9 to both sides:
$8 = 2n$
$n = 4$ (does not match $n=-4$)

Step3: Test Option 2

Solve $1 = 0.75n + 3.25$.
Subtract 3.25 from both sides:
$1 - 3.25 = 0.75n$
$-2.25 = 0.75n$
$n = \frac{-2.25}{0.75} = -3$ (does not match $n=-4$)

Step4: Test Option 3

Solve $3 - 6n + 3n = -3 + 4 - 4n$.
Simplify both sides:
$3 - 3n = 1 - 4n$
Add $4n$ to both sides:
$3 + n = 1$
Subtract 3 from both sides:
$n = 1 - 3 = -2$ (does not match $n=-4$)

Step5: Test Option 4

Solve $\frac{11}{4}n + 2 = -3 + \frac{3}{2}n$.
Convert $\frac{3}{2}$ to $\frac{6}{4}$ to align denominators:
$\frac{11}{4}n + 2 = -3 + \frac{6}{4}n$
Subtract $\frac{6}{4}n$ from both sides:
$\frac{5}{4}n + 2 = -3$
Subtract 2 from both sides:
$\frac{5}{4}n = -5$
Multiply both sides by $\frac{4}{5}$:
$n = -5 \times \frac{4}{5} = -4$ (matches the original solution)

Answer:

$\boldsymbol{\frac{11}{4}n + 2 = -3 + \frac{3}{2}n}$