Alright, let's solve each of these equations step-by-step:
i) [tex]\( 5x = 20 \)[/tex]
To isolate [tex]\( x \)[/tex], divide both sides by 5:
[tex]\[
x = \frac{20}{5} = 4.0
\][/tex]
ii) [tex]\( 6x = 18 \)[/tex]
To isolate [tex]\( x \)[/tex], divide both sides by 6:
[tex]\[
x = \frac{18}{6} = 3.0
\][/tex]
iii) [tex]\( x + 8 = 15 \)[/tex]
To isolate [tex]\( x \)[/tex], subtract 8 from both sides:
[tex]\[
x = 15 - 8 = 7
\][/tex]
iv) [tex]\( x + 8 = 5 \)[/tex]
To isolate [tex]\( x \)[/tex], subtract 8 from both sides:
[tex]\[
x = 5 - 8 = -3
\][/tex]
v) [tex]\( 2x + 8 = 15 \)[/tex]
First, subtract 8 from both sides:
[tex]\[
2x = 15 - 8
\][/tex]
Next, divide both sides by 2:
[tex]\[
x = \frac{7}{2} = 3.5
\][/tex]
vi) [tex]\( 8 - x = 4 \)[/tex]
First, subtract 4 from both sides:
[tex]\[
8 - 4 = x
\][/tex]
[tex]\[
x = 4
\][/tex]
vii) [tex]\( 2x - 3 = 9 \)[/tex]
First, add 3 to both sides:
[tex]\[
2x = 9 + 3
\][/tex]
Next, divide both sides by 2:
[tex]\[
x = \frac{12}{2} = 6.0
\][/tex]
viii) [tex]\( 20x - 35 = 15 \)[/tex]
First, add 35 to both sides:
[tex]\[
20x = 15 + 35
\][/tex]
Next, divide both sides by 20:
[tex]\[
x = \frac{50}{20} = 2.5
\][/tex]
ix) [tex]\( 8 - y = 2 - 3y \)[/tex]
First, add [tex]\( 3y \)[/tex] to both sides:
[tex]\[
8 + 2y = 2
\][/tex]
Then subtract 8 from both sides:
[tex]\[
2y = 2 - 8
\][/tex]
[tex]\[
2y = -6
\][/tex]
Finally, divide both sides by 2:
[tex]\[
y = \frac{-6}{2} = -3.0
\][/tex]
x) [tex]\( 4x + 1 = 2x + 9 \)[/tex]
First, subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[
2x + 1 = 9
\][/tex]
Then subtract 1 from both sides:
[tex]\[
2x = 8
\][/tex]
Finally, divide both sides by 2:
[tex]\[
x = \frac{8}{2} = 4.0
\][/tex]
xi) [tex]\( 3x + 4 = 7 - 2x \)[/tex]
First, add [tex]\( 2x \)[/tex] to both sides:
[tex]\[
5x + 4 = 7
\][/tex]
Then subtract 4 from both sides:
[tex]\[
5x = 3
\][/tex]
Finally, divide both sides by 5:
[tex]\[
x = \frac{3}{5} = 0.6
\][/tex]
xii) [tex]\( 3 - x = 8x + 12 \)[/tex]
First, add [tex]\( x \)[/tex] to both sides:
[tex]\[
3 = 9x + 12
\][/tex]
Then subtract 12 from both sides:
[tex]\[
-9 = 9x
\][/tex]
Finally, divide both sides by 9:
[tex]\[
x = \frac{-9}{9} = -1.0
\][/tex]
xiii) [tex]\( 4x + 2 = 11x - 12 \)[/tex]
First, subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[
2 = 7x - 12
\][/tex]
Then add 12 to both sides:
[tex]\[
14 = 7x
\][/tex]
Finally, divide both sides by 7:
[tex]\[
x = \frac{14}{7} = 2.0
\][/tex]
xiv) [tex]\( 4 - 3y = 16 + 5y \)[/tex]
First, subtract [tex]\( 4 \)[/tex] from both sides:
[tex]\[
-3y = 12 + 5y
\][/tex]
Then add [tex]\( 3y \)[/tex] to both sides:
[tex]\[
0 = 8y
\][/tex]
Finally, divide both sides by 8:
[tex]\[
y = \frac{0}{8}
\][/tex]
xv) [tex]\( 2 - 7t = 8 - 3t \)[/tex]
First, add [tex]\( 7t \)[/tex] to both sides:
[tex]\[
2 = 8 + 4t
\][/tex]
Then subtract 8 from both sides:
[tex]\[
-6 = 4t
\][/tex]
Finally, divide both sides by 4:
[tex]\[
t = \frac{-6}{4} = -1.5
\][/tex]
xvi) [tex]\( 3y - 7 = 19 - y \)[/tex]
First, add [tex]\( y \)[/tex] to both sides:
[tex]\[
4y - 7 = 19
\][/tex]
Then add 7 to both sides:
[tex]\[
4y = 26
\][/tex]
Finally, divide both sides by 4:
[tex]\[
y = \frac{26}{4} = 6.5
\][/tex]
These steps provide the solutions for each given equation.
