Question

Help me I've been stuck forever! it is an absolute value equation btw.​

Answer 1

Answer:

${n=\frac{-11}{3} ,3}$

Step-by-step explanation:

Original problem: $2|n+7|=|4n+8|$

Get rid of the absolute value signs by breaking the problem down into two equations, the positive and negative cases.

The first case, the positive case, will be formed by just changing the absolute value symbols ($|$) into parentheses.

$2(n+7)=(4n+8)$

The next case, the negative case, will be formed by changing the absolute value symbols into parentheses as well but the $(4n+8)$ will be multiplied by negative 1.

$2(n+7)=-(4n+8)$

Let's solve the first equation we created with the positive case. Start by getting rid of the parentheses on the right side of the equation.

$2(n+7)=4n+8$

Distribute 2 inside the parentheses.

$2n+14=4n+8$

Combine like terms by subtracting 2n and 8 from both sides of the equation.

$6=2n$

Isolate and solve for n by dividing both sides of the equation by 2.

$3=n$

One of the solutions is 3. Let's solve the second equation we created. Distribute the negative sign inside the parentheses on the right side of the equation.

$2(n+7)=-4n-8$

Now distribute 2 inside the parentheses on the left side of the equation.

$2n+14=-4n-8$

Combine like terms by adding 4n to both sides of the equation.

$6n+14=-8$

Subtract 14 from both sides of the equation.

$6n=-22$

Divide both sides of the equation by 6.

$n=\frac{-22}{6}$

This fraction can be simplified by dividing the top and bottom by 2 to $\frac{-11}{3}$.

You can check for extraneous solutions by substituting 3 and $\frac{-11}{3}$ back into the original equation. There are no extraneous solutions in this particular problem.

This means that the two solutions of n are 3 and $\frac{-11}{3}$.

$\boxed{n=\frac{-11}{3} ,3}$