solve for n. |3n+5|=7
See above.
2/3
To solve the equation |3n + 5| = 7, we will consider two cases: one where the expression inside the absolute value is positive and another where it is negative.
Case 1: 3n + 5 is positive
In this case, we can drop the absolute value symbols and rewrite the equation as:
3n + 5 = 7
Now we can solve for n:
3n = 7 - 5
3n = 2
n = 2/3
Case 2: 3n + 5 is negative
In this case, we need to negate the expression inside the absolute value, so we will rewrite the equation as:
-(3n + 5) = 7
Distribute the negative sign to both terms inside the parentheses:
-3n - 5 = 7
Add 5 to both sides to isolate the variable:
-3n = 7 + 5
-3n = 12
Divide both sides by -3:
n = 12 / -3
n = -4
Therefore, the solutions for n are n = 2/3 and n = -4.