Sure! Let's solve each equation step-by-step.
### Question 14: [tex]\( 5n + 34 = -2(1 - 7n) \)[/tex]
1. Distribute the [tex]\(-2\)[/tex] on the right side:
[tex]\[
5n + 34 = -2 + 14n
\][/tex]
2. Move all terms involving [tex]\( n \)[/tex] to one side and constants to the other side:
[tex]\[
5n - 14n = -2 - 34
\][/tex]
3. Simplify both sides:
[tex]\[
-9n = -36
\][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides by [tex]\(-9\)[/tex]:
[tex]\[
n = \frac{-36}{-9} = 4
\][/tex]
The solution is [tex]\( n = 4 \)[/tex].
### Question 16: [tex]\( 3n - 5 = -8(6 + 5n) \)[/tex]
1. Distribute the [tex]\(-8\)[/tex] on the right side:
[tex]\[
3n - 5 = -48 - 40n
\][/tex]
2. Move all terms involving [tex]\( n \)[/tex] to one side and constants to the other side:
[tex]\[
3n + 40n = -48 + 5
\][/tex]
3. Simplify both sides:
[tex]\[
43n = -43
\][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides by [tex]\( 43 \)[/tex]:
[tex]\[
n = \frac{-43}{43} = -1
\][/tex]
The solution is [tex]\( n = -1 \)[/tex].
### Question 18: [tex]\( -3(4x + 3) + 4(6x + 1) = 43 \)[/tex]
1. Distribute the [tex]\(-3\)[/tex] and the [tex]\(4\)[/tex] on the left side:
[tex]\[
-12x - 9 + 24x + 4 = 43
\][/tex]
2. Combine like terms on the left side:
[tex]\[
(-12x + 24x) + (-9 + 4) = 43
\][/tex]
[tex]\[
12x - 5 = 43
\][/tex]
3. Move the constant term to the other side:
[tex]\[
12x = 43 + 5
\][/tex]
[tex]\[
12x = 48
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 12 \)[/tex]:
[tex]\[
x = \frac{48}{12} = 4
\][/tex]
The solution is [tex]\( x = 4 \)[/tex].
