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Sagot :
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.
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.
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