aryana simplified the expression 3(x + 4) + 2(2x - 3). she justified her work by letting x = 3 in both the…

aryana simplified the expression 3(x + 4) + 2(2x - 3). she justified her work by letting x = 3 in both the given and simplified expressions. which is the correct simplified expression for aryanas expression? what is the result for both expressions when x = 3?

aryana simplified the expression 3(x + 4) + 2(2x - 3). she justified her work by letting x = 3 in both the given and simplified expressions. which is the correct simplified expression for aryanas expression? what is the result for both expressions when x = 3?

Answer

Explanation:

Step1: Expand the given expression

[ \begin{align*} 3(x + 4)+2(2x - 3)&=3\times x+3\times4+2\times2x-2\times3\ &=3x + 12+4x-6 \end{align*} ]

Step2: Combine like - terms

[ \begin{align*} 3x + 12+4x-6&=(3x + 4x)+(12 - 6)\ &=7x+6 \end{align*} ]

Step3: Evaluate the original and simplified expressions at (x = 3)

For the original expression (3(x + 4)+2(2x - 3)):

[ \begin{align*} 3(3 + 4)+2(2\times3 - 3)&=3\times7+2\times(6 - 3)\ &=21+2\times3\ &=21 + 6\ &=27 \end{align*} ]

For the simplified expression (7x+6):

When (x = 3), (7\times3+6=21 + 6=27)

Answer:

The correct simplified expression is (7x + 6). The result for both expressions when (x = 3) is (27).