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
the equation has no solution
A value of xx that makes the equation false is
, which when substituted into the equation and simplified makes the equation turn into
equals=
.
Another value of xx that makes the equation false is
, which when substituted into the equation and simplified makes the equation turn into
equals=
.
To determine whether the equation has a one solution, no solutions, or an infinite number of solutions, we can simplify and solve the equation:
2(x+3)=2x+6
Expanding the equation:
2x + 6 = 2x + 6
Subtracting 2x from both sides:
6 = 6
We can see that the equation simplifies to 6 = 6. This means that both sides of the equation are equal. Therefore, there are an infinite number of solutions for this equation.
Since there are an infinite number of solutions, any value of x can be substituted into the equation and it will still hold true. Two examples of values that support this conclusion are:
x = 0:
2(0+3) = 2(0) + 6
6 = 6
x = 5:
2(5+3) = 2(5) + 6
16 = 16