Alright, let's solve each part of the question step-by-step.
### Part (a): Solving [tex]\( 4(x + 3) = 18 \)[/tex]
1. Distribute the 4 on the left side:
[tex]\[
4x + 12 = 18
\][/tex]
2. Subtract 12 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
4x + 12 - 12 = 18 - 12
\][/tex]
[tex]\[
4x = 6
\][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{4} = \frac{3}{2}
\][/tex]
So the solution for part (a) is:
[tex]\[ x = \frac{3}{2} \][/tex]
### Part (b): Solving [tex]\( -2(y + 3) = 8 \)[/tex]
1. Distribute the -2 on the left side:
[tex]\[
-2y - 6 = 8
\][/tex]
2. Add 6 to both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[
-2y - 6 + 6 = 8 + 6
\][/tex]
[tex]\[
-2y = 14
\][/tex]
3. Divide both sides by -2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{14}{-2} = -7
\][/tex]
So the solution for part (b) is:
[tex]\[ y = -7 \][/tex]
### Construct 3 equations with [tex]\( t = -9 \)[/tex]
Let's consider [tex]\( t \)[/tex] equations and solve one of them:
[tex]\[ 3t + 18 = -9 \][/tex]
1. Isolate the term with [tex]\( t \)[/tex]:
[tex]\[
3t + 18 = -9
\][/tex]
2. Subtract 18 from both sides:
[tex]\[
3t + 18 - 18 = -9 - 18
\][/tex]
[tex]\[
3t = -27
\][/tex]
3. Divide both sides by 3 to solve for [tex]\( t \)[/tex]:
[tex]\[
t = \frac{-27}{3} = -9
\][/tex]
So [tex]\( t = -9 \)[/tex] correctly satisfies the equation.
### Solving [tex]\( 6x - 2 = 7x - 8 \)[/tex]
1. First, we need to move all terms involving [tex]\( x \)[/tex] to one side of the equation:
[tex]\[
6x - 2 = 7x - 8
\][/tex]
2. Subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[
-2 = x - 8
\][/tex]
3. Add 8 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
-2 + 8 = x - 8 + 8
\][/tex]
[tex]\[
x = 6
\][/tex]
So the solution for [tex]\( x \)[/tex] is:
[tex]\[ x = 6 \][/tex]
### Checking which option matches [tex]\( x = 6 \)[/tex]
Given the options:
a) 6
b) 4
c) 5
The correct option here is:
[tex]\[ \boxed{a)} \][/tex]
