Final answer:
To solve the equation |2n+4|=8, we create two separate equations: 2n+4=8 and 2n+4=-8. Solving these two equations gives us the possible values for n, which are 2 and -6.
Step-by-step explanation:
To solve the equation |2n+4|=8, we need to consider that the absolute value function splits the equation into two separate cases. The absolute value of an expression is equal to 8 either if the expression itself is 8 or if its negation (opposite in sign) is 8. Thus:
- For the positive case, we drop the absolute value and solve the equation as it is: 2n + 4 = 8.
- For the negative case, we drop the absolute value, negate the inside of the absolute value, and then solve: 2n + 4 = -8.
Now, we solve each of these two equations as follows:
- 2n + 4 = 8: Subtract 4 from both sides to get 2n = 4, then divide by 2 to find n = 2.
- 2n + 4 = -8: Subtract 4 from both sides to get 2n = -12, then divide by 2 to find n = -6.
Therefore, the possible values of n that satisfy the original equation are n = 2 and n = -6.