Question

1. Are equations (3x+9)=6 and x+3=2 equivalent?

Answer 1

Answer:

1.) Yes

2.) No (unless x=-3)

3.) Yes

4.) No (unless x=3)

Step-by-step explanation:

1.) 3x+9=6 is equivalent to x+3=2

$3x+9=6\\3x+9-9=6-9\\3x=-3\\\frac{3x}{3}=\frac{-3}{3}\\x=-1\\\\x+3=2\\x+3-3=2-3\\x=-1$

$3x+9=6\\3(x+3)=6\\\frac{3(x+3)}{3}=\frac{6}{3}\\x+3=2$

2.) 3x+9 is not equivalent to x+3 unless x=-3

$3x+9\\3(x+3)\neq x+3$

3.) $\frac{x}{(x-2)}=4$ is equivalent to x=4(x-2)

$\frac{x}{(x-2)}=4\\(x-2)\frac{x}{(x-2)}=4(x-2)\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\3x=8\\x=\frac{8}{3}\\\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\8=3x\\x=8/3$

$\frac{x}{(x-2)}=4\\(x-2)\frac{x}{(x-2)}=4(x-2)\\x=4(x-2)$

4.) These two expressions could only be equivalent if x=3