Answered

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TSUA Mathematics College and Career Readiness - Question 1 of 20

Instructions:
Use the paper you were given to write the correct answer if necessary.

Question:
Which of the following is equivalent to [tex]$12x + 8$[/tex]?

A. [tex]$4(3x + 2)$[/tex]
B. [tex]$4(3x + 8)$[/tex]
C. [tex]$4(3x + 2x)$[/tex]
D. [tex]$20x$[/tex]

Sagot :

GinnyAnswer
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].
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