Answer:
[tex]\textsf{(a)} \quad -2x-4[/tex]
[tex]\textsf{(b)} \quad 2x+5[/tex]
(c) Not equivalent.
[tex]\textsf{(d)} \quad 3x^2-24x+48[/tex]
[tex]\textsf{(e)} \quad 9x^2-72x+144[/tex]
(f) Not equivalent.
Step-by-step explanation:
Equivalent expressions are expressions that simplify to the same expression.
Part (a)
[tex]\begin{aligned}&\textsf{Add 3 to $x$}: & \quad x+3\\&\textsf{Subtract the result from $1$}: & \quad 1-(x+3)\\&\textsf{Double}: & \quad 2[1-(x+3)]\\&\textsf{Expand}: & \quad 2[1-x-3]\\&\textsf{Simplify}:&2[-x-2]\\&& -2x-4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}&\textsf{Add 3 to $x$}: & \quad x+3\\&\textsf{Double}: & \quad 2(x+3)\\&\textsf{Subtract $1$ from the result}: & \quad 2(x+3)-1\\&\textsf{Expand}: & 2x+6-1\\&\textsf{Simplify}:&2x+5\end{aligned}[/tex]
Part (c)
The expressions are not equivalent.
The coefficients of the x-variables are the negatives of one another, and the constants are different numbers.
Part (d)
[tex]\begin{aligned}&\textsf{Subtract 4 from $x$}: & \quad x-4\\&\textsf{Square the result}: & \quad (x-4)^2\\&\textsf{Triple}: & \quad 3(x-4)^2\\&\textsf{Expand}: & \quad 3(x^2-8x+16)\\&\textsf{Simplify}:& 3x^2-24x+48\end{aligned}[/tex]
Part (e)
[tex]\begin{aligned}&\textsf{Subtract 4 from $x$}: & \quad x-4\\&\textsf{Triple the result}: & \quad 3(x-4)\\&\textsf{Square}: & \quad [3(x-4)]^2\\&\textsf{Expand}: & \quad [3x-12]^2\\&\textsf{Simplify}:& 9x^2-72x+144\end{aligned}[/tex]
Part (f)
The expressions are not equivalent.
The coefficients the second equation are three times the coefficients of the first equation.
