Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
2(x+3)=2x+6
then complete the following statement
A value of xx that makes the equation true is
, which when substituted into the equation and simplified makes the equation turn into
equals=
.
A value of xx that makes the equation false is
, which when substituted into the equation and simplified makes the equation turn into
equals=
.
The equation 2(x+3)=2x+6 has one solution.
A value of x that makes the equation true is 0, which when substituted into the equation and simplified makes the equation turn into 2(0+3)=2(0)+6. This simplifies to 2(3)=0+6, which becomes 6=6.
A value of x that makes the equation false is any value other than 0. For example, if we substitute x=1 into the equation, we get 2(1+3)=2(1)+6. This simplifies to 2(4)=2+6, which becomes 8=8. Since 8=8 is true, x=1 does not make the equation false. Thus, any value other than 0 would make the equation true.