Answer :
To solve the equation [tex]\( 6(x - 5) = 4x + 20 \)[/tex], let's go through the steps in detail:
1. Apply the distributive property to the left side of the equation:
[tex]\[ 6(x - 5) = 6x - 30 \][/tex]
Now your equation looks like this:
[tex]\[ 6x - 30 = 4x + 20 \][/tex]
2. Move all terms with [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side. First, subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 6x - 4x - 30 = 20 \][/tex]
Simplifying this gives:
[tex]\[ 2x - 30 = 20 \][/tex]
3. Next, add 30 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x - 30 + 30 = 20 + 30 \][/tex]
Simplifying this gives:
[tex]\[ 2x = 50 \][/tex]
4. Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{50}{2} \][/tex]
This simplifies to:
[tex]\[ x = 25 \][/tex]
So, the correct answer is [tex]\( \boxed{25} \)[/tex]. Therefore, the correct option from the given choices is:
C. [tex]\( x = 25 \)[/tex]
1. Apply the distributive property to the left side of the equation:
[tex]\[ 6(x - 5) = 6x - 30 \][/tex]
Now your equation looks like this:
[tex]\[ 6x - 30 = 4x + 20 \][/tex]
2. Move all terms with [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side. First, subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 6x - 4x - 30 = 20 \][/tex]
Simplifying this gives:
[tex]\[ 2x - 30 = 20 \][/tex]
3. Next, add 30 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 2x - 30 + 30 = 20 + 30 \][/tex]
Simplifying this gives:
[tex]\[ 2x = 50 \][/tex]
4. Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{50}{2} \][/tex]
This simplifies to:
[tex]\[ x = 25 \][/tex]
So, the correct answer is [tex]\( \boxed{25} \)[/tex]. Therefore, the correct option from the given choices is:
C. [tex]\( x = 25 \)[/tex]
