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

Respuesta :

hello

the first equation given was

[tex]-11(x-2)=8x-2=8+11[/tex]

let's resolve each side of the equations

for the first one,

[tex]\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} \\ \frac{19x}{19}=\frac{24}{19} \\ x=\frac{24}{19} \end{gathered}[/tex]

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

[tex]\begin{gathered} 8x-2=8+11 \\ 8x-2=19 \\ 8x=19+2 \\ 8x=21 \\ \text{divide both sides by the coeffiecient of x} \\ \frac{8x}{8}=\frac{21}{8} \\ x=\frac{21}{8} \end{gathered}[/tex]

from the calculations above, the two equations are not equal

[tex]\frac{24}{19}\ne\frac{21}{8}[/tex]