Answered

Which of the following is an equivalent simplified expression for [tex]2(4x + 7) - 3(2x - 4)[/tex]?

A. [tex]3x + 10[/tex]

B. [tex]2x + 26[/tex]

C. [tex]3x + 11[/tex]

D. [tex]2x + 2[/tex]

E. [tex]x + 2[/tex]



Answer :

GinnyAnswer
To simplify the expression [tex]\( 2(4x + 7) - 3(2x - 4) \)[/tex], we need to follow a few algebraic steps. Let's break it down step-by-step.

1. Distribute the 2 in the first term [tex]\( 2(4x + 7) \)[/tex]:

[tex]\[ 2(4x + 7) = 2 \cdot 4x + 2 \cdot 7 = 8x + 14 \][/tex]

2. Distribute the 3 in the second term [tex]\( -3(2x - 4) \)[/tex]:

[tex]\[ -3(2x - 4) = -3 \cdot 2x + (-3) \cdot (-4) = -6x + 12 \][/tex]

3. Combine the distributed terms:

The original expression is now:

[tex]\[ 8x + 14 - 6x + 12 \][/tex]

4. Combine like terms:

Group the [tex]\( x \)[/tex] terms and constant terms together:

[tex]\[ (8x - 6x) + (14 + 12) \][/tex]

Simplify the grouped terms:

[tex]\[ 2x + 26 \][/tex]

So, the simplified expression for [tex]\( 2(4x + 7) - 3(2x - 4) \)[/tex] is [tex]\( 2x + 26 \)[/tex].

Thus, the correct answer is [tex]\( 2x + 26 \)[/tex].