Answer :
To determine which expression is equivalent to \( 12x + 8 \), we need to simplify each given option and compare it with \( 12x + 8 \).
Let's evaluate each option step-by-step.
Option 1: \( 4(3x + 2) \)
[tex]\[ 4(3x + 2) = 4 \cdot 3x + 4 \cdot 2 = 12x + 8 \][/tex]
This matches the given expression \( 12x + 8 \).
Option 2: \( 4(3x + 8) \)
[tex]\[ 4(3x + 8) = 4 \cdot 3x + 4 \cdot 8 = 12x + 32 \][/tex]
This does not match the given expression \( 12x + 8 \).
Option 3: \( 4(3x + 2x) \)
[tex]\[ 4(3x + 2x) = 4 \cdot 5x = 20x \][/tex]
This does not match \( 12x + 8 \).
Option 4: \( 20x \)
[tex]\[ 20x \][/tex]
This also does not match \( 12x + 8 \).
From the analysis above, the only option that simplifies exactly to \( 12x + 8 \) is:
[tex]\[ 4(3x + 2) \][/tex]
Thus, Option 1: [tex]\( 4(3x + 2) \)[/tex] is equivalent to [tex]\( 12x + 8 \)[/tex].
Let's evaluate each option step-by-step.
Option 1: \( 4(3x + 2) \)
[tex]\[ 4(3x + 2) = 4 \cdot 3x + 4 \cdot 2 = 12x + 8 \][/tex]
This matches the given expression \( 12x + 8 \).
Option 2: \( 4(3x + 8) \)
[tex]\[ 4(3x + 8) = 4 \cdot 3x + 4 \cdot 8 = 12x + 32 \][/tex]
This does not match the given expression \( 12x + 8 \).
Option 3: \( 4(3x + 2x) \)
[tex]\[ 4(3x + 2x) = 4 \cdot 5x = 20x \][/tex]
This does not match \( 12x + 8 \).
Option 4: \( 20x \)
[tex]\[ 20x \][/tex]
This also does not match \( 12x + 8 \).
From the analysis above, the only option that simplifies exactly to \( 12x + 8 \) is:
[tex]\[ 4(3x + 2) \][/tex]
Thus, Option 1: [tex]\( 4(3x + 2) \)[/tex] is equivalent to [tex]\( 12x + 8 \)[/tex].
