Answer :
To determine which expression is not equivalent to [tex]\(6x + 18\)[/tex], we need to simplify each of the given choices and compare them to [tex]\(6x + 18\)[/tex].
Choice (1): [tex]\(4x + 10 + 2x + 8\)[/tex]
Let's simplify this expression step-by-step:
[tex]\[ 4x + 10 + 2x + 8 \][/tex]
Combine the like terms:
[tex]\[ (4x + 2x) + (10 + 8) \][/tex]
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(4x + 10 + 2x + 8\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
Choice (2): [tex]\(10x + 20 - 2x + 2\)[/tex]
Let's simplify this expression:
[tex]\[ 10x + 20 - 2x + 2 \][/tex]
Combine the like terms:
[tex]\[ (10x - 2x) + (20 + 2) \][/tex]
[tex]\[ 8x + 22 \][/tex]
So, [tex]\(10x + 20 - 2x + 2\)[/tex] simplifies to [tex]\(8x + 22\)[/tex] and is not equivalent to [tex]\(6x + 18\)[/tex].
Choice (3): [tex]\(6(x + 3)\)[/tex]
Let's expand this expression:
[tex]\[ 6(x + 3) \][/tex]
Use the distributive property:
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(6(x + 3)\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
Choice (4): [tex]\(2(3x + 9)\)[/tex]
Let's expand this expression:
[tex]\[ 2(3x + 9) \][/tex]
Use the distributive property:
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(2(3x + 9)\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
After comparing all choices, the only expression not equivalent to [tex]\(6x + 18\)[/tex] is Choice (2): [tex]\(10x + 20 - 2x + 2\)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{2} \][/tex]
Choice (1): [tex]\(4x + 10 + 2x + 8\)[/tex]
Let's simplify this expression step-by-step:
[tex]\[ 4x + 10 + 2x + 8 \][/tex]
Combine the like terms:
[tex]\[ (4x + 2x) + (10 + 8) \][/tex]
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(4x + 10 + 2x + 8\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
Choice (2): [tex]\(10x + 20 - 2x + 2\)[/tex]
Let's simplify this expression:
[tex]\[ 10x + 20 - 2x + 2 \][/tex]
Combine the like terms:
[tex]\[ (10x - 2x) + (20 + 2) \][/tex]
[tex]\[ 8x + 22 \][/tex]
So, [tex]\(10x + 20 - 2x + 2\)[/tex] simplifies to [tex]\(8x + 22\)[/tex] and is not equivalent to [tex]\(6x + 18\)[/tex].
Choice (3): [tex]\(6(x + 3)\)[/tex]
Let's expand this expression:
[tex]\[ 6(x + 3) \][/tex]
Use the distributive property:
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(6(x + 3)\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
Choice (4): [tex]\(2(3x + 9)\)[/tex]
Let's expand this expression:
[tex]\[ 2(3x + 9) \][/tex]
Use the distributive property:
[tex]\[ 6x + 18 \][/tex]
So, [tex]\(2(3x + 9)\)[/tex] simplifies to [tex]\(6x + 18\)[/tex] and is equivalent to the given expression.
After comparing all choices, the only expression not equivalent to [tex]\(6x + 18\)[/tex] is Choice (2): [tex]\(10x + 20 - 2x + 2\)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{2} \][/tex]
