To solve the equation [tex]\( 5n + 34 = -2(1 - 7n) \)[/tex], follow these steps:
1. First, distribute the [tex]\(-2\)[/tex] on the right side of the equation:
[tex]\[
-2(1 - 7n) = -2 \cdot 1 + (-2) \cdot (-7n) = -2 + 14n
\][/tex]
2. Rewrite the equation with the distributed terms:
[tex]\[
5n + 34 = -2 + 14n
\][/tex]
3. To isolate the terms involving [tex]\( n \)[/tex], subtract [tex]\( 14n \)[/tex] from both sides of the equation:
[tex]\[
5n - 14n + 34 = -2
\][/tex]
Simplify this to:
[tex]\[
-9n + 34 = -2
\][/tex]
4. Next, move the constant term to one side by subtracting 34 from both sides:
[tex]\[
-9n = -2 - 34
\][/tex]
Simplify the right side:
[tex]\[
-9n = -36
\][/tex]
5. To solve for [tex]\( n \)[/tex], divide both sides by [tex]\(-9\)[/tex]:
[tex]\[
n = \frac{-36}{-9}
\][/tex]
6. Simplify the fraction:
[tex]\[
n = 4
\][/tex]
So, the solution to the equation is:
[tex]\[
n = 4
\][/tex]
