Question

1) For the following pairs equations explain why the equations are equivalent (or not) -11(x-2)=8 x-2=8+11 2)For the following pairs of equations explain why the equations are equivalent. (Or Not!) -3(2x+9)=12 2x+9=-4

Answer 1

hello

the first equation given was

`-11(x-2)=8x-2=8+11`

let's resolve each side of the equations

for the first one,

`\begin{gathered} -11(x-2)=8x-2 \\ -11x+22=8x-2 \\ \text{collect like terms} \\ 8x+11x=22+2 \\ 19x=24 \\ \text{divide both sides by coefficient of x} \\ (19x)/(19)=(24)/(19) \\ x=(24)/(19) \end{gathered}`

now let's test for the other side of the equation

`\begin{gathered} 8x-2=8+11 \\ 8x-2=19 \\ 8x=19+2 \\ 8x=21 \\ \text{divide both sides by the coeffiecient of x} \\ (8x)/(8)=(21)/(8) \\ x=(21)/(8) \end{gathered}`

from the calculations above, the two equations are not equal

`(24)/(19)\\e(21)/(8)`