Select the correct answer. Consider the equation below. $$ -5 n+31=-14 n-5 $$ Select the equation that has the same solution. $$ \begin{array}{l}11 \ ext { ( }-1-22 n+2=-3+\frac{3}{2} n \ 3-6 n+3 n=-3+4-4 n \ 1=0.75 n+3.25\end{array} $$

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Select the correct answer. Consider the equation below. $$ -5 n+31=-14 n-5 $$ Select the equation that has the same solution. $$ \begin{array}{l}11 \ 	ext { ( }-1-22 n+2=-3+\frac{3}{2} n \ 3-6 n+3 n=-3+4-4 n \ 1=0.75 n+3.25\end{array} $$

UpStudy AI · Accepted Answer

We need to solve the equation $$ -5n + 31 = -14n - 5 $$ to find its solution.
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$-5n+31=-14n-5$$
- step1: Move the expression to the left side:
  $$-5n+14n=-5-31$$
- step2: Add and subtract:
  $$9n=-5-31$$
- step3: Add and subtract:
  $$9n=-36$$
- step4: Divide both sides:
  $$\frac{9n}{9}=\frac{-36}{9}$$
- step5: Divide the numbers:
  $$n=-4$$
We found that the solution to the equation $$ -5n + 31 = -14n - 5 $$ is $$ n = -4 $$. Now, we will check each of the provided equations to see which one also has the solution $$ n = -4 $$.
For the equation $$ -1 - 22n + 2 = -3 + \frac{3}{2}n $$:
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$-1-22n+2=-3+\frac{3}{2}n$$
- step1: Add the numbers:
  $$1-22n=-3+\frac{3}{2}n$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(1-22night)	imes 2=\left(-3+\frac{3}{2}night)	imes 2$$
- step3: Calculate:
  $$2-44n=\left(-3+\frac{3}{2}night)	imes 2$$
- step4: Calculate:
  $$2-44n=-6+3n$$
- step5: Move the expression to the left side:
  $$-44n-3n=-6-2$$
- step6: Add and subtract:
  $$-47n=-6-2$$
- step7: Add and subtract:
  $$-47n=-8$$
- step8: Change the signs:
  $$47n=8$$
- step9: Divide both sides:
  $$\frac{47n}{47}=\frac{8}{47}$$
- step10: Divide the numbers:
  $$n=\frac{8}{47}$$
The second equation is $$ 3 - 6n + 3n = -3 + 4 - 4n $$:
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$3-6n+3n=-3+4-4n$$
- step1: Add the terms:
  $$3-3n=1-4n$$
- step2: Move the expression to the left side:
  $$-3n+4n=1-3$$
- step3: Add and subtract:
  $$n=1-3$$
- step4: Add and subtract:
  $$n=-2$$
The third equation is $$ 1 = 0.75n + 3.25 $$:
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$1=0.75n+3.25$$
- step1: Swap the sides:
  $$0.75n+3.25=1$$
- step2: Move the constant to the right side:
  $$0.75n=1-3.25$$
- step3: Subtract the numbers:
  $$0.75n=-2.25$$
- step4: Divide both sides:
  $$\frac{0.75n}{0.75}=\frac{-2.25}{0.75}$$
- step5: Divide the numbers:
  $$n=-3$$
We have the following results for the equations checked:
1. $$ -1 - 22n + 2 = -3 + \frac{3}{2}n $$ gives $$ n = \frac{8}{47} $$
2. $$ 3 - 6n + 3n = -3 + 4 - 4n $$ gives $$ n = -2 $$
3. $$ 1 = 0.75n + 3.25 $$ gives $$ n = -3 $$

None of these equations yield the solution $$ n = -4 $$. Therefore, none of the provided equations have the same solution as the original equation.
No equation from the options has the same solution as $$ -5n + 31 = -14n - 5 $$.

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Select the equation that has the same solution.

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