Answer :
To solve the given equations for [tex]\( x \)[/tex], let's check each one systematically:
1. Equation 1: [tex]\( 18x = 126 \)[/tex]
- To solve for [tex]\( x \)[/tex], divide both sides by 18:
[tex]\[
x = \frac{126}{18} = 7
\][/tex]
2. Equation 2: [tex]\( 3x + 6 = 126 \)[/tex]
- Start by subtracting 6 from both sides:
[tex]\[
3x = 126 - 6 = 120
\][/tex]
- Then, divide both sides by 3:
[tex]\[
x = \frac{120}{3} = 40
\][/tex]
3. Equation 3: [tex]\( 3(x + 6) = 126 \)[/tex]
- First, divide both sides by 3 to simplify:
[tex]\[
x + 6 = \frac{126}{3} = 42
\][/tex]
- Next, subtract 6 from both sides:
[tex]\[
x = 42 - 6 = 36
\][/tex]
4. Equation 4: [tex]\( x + 18 = 126 \)[/tex]
- Subtract 18 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 126 - 18 = 108
\][/tex]
From these solutions, you can see the solutions are [tex]\( x = 7 \)[/tex], [tex]\( x = 40 \)[/tex], [tex]\( x = 36 \)[/tex], and [tex]\( x = 108 \)[/tex] for equations 1, 2, 3, and 4, respectively.
1. Equation 1: [tex]\( 18x = 126 \)[/tex]
- To solve for [tex]\( x \)[/tex], divide both sides by 18:
[tex]\[
x = \frac{126}{18} = 7
\][/tex]
2. Equation 2: [tex]\( 3x + 6 = 126 \)[/tex]
- Start by subtracting 6 from both sides:
[tex]\[
3x = 126 - 6 = 120
\][/tex]
- Then, divide both sides by 3:
[tex]\[
x = \frac{120}{3} = 40
\][/tex]
3. Equation 3: [tex]\( 3(x + 6) = 126 \)[/tex]
- First, divide both sides by 3 to simplify:
[tex]\[
x + 6 = \frac{126}{3} = 42
\][/tex]
- Next, subtract 6 from both sides:
[tex]\[
x = 42 - 6 = 36
\][/tex]
4. Equation 4: [tex]\( x + 18 = 126 \)[/tex]
- Subtract 18 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 126 - 18 = 108
\][/tex]
From these solutions, you can see the solutions are [tex]\( x = 7 \)[/tex], [tex]\( x = 40 \)[/tex], [tex]\( x = 36 \)[/tex], and [tex]\( x = 108 \)[/tex] for equations 1, 2, 3, and 4, respectively.
