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, left bracket, x, plus, 3, right bracket, equals, 2, x, plus, 6
2(x+3)=
2x+6
The equation 2(x+3) = 2x + 6 has a one solution.
To support this conclusion, let's solve the equation:
2(x+3) = 2x + 6
2x + 6 = 2x + 6 [Distributive property]
2x - 2x + 6 = 2x - 2x + 6 [Subtract 2x from both sides]
6 = 6 [Simplify]
Based on the simplified equation 6 = 6, we can see that both sides are equal. Therefore, this equation has one solution.
Two values of x that support this conclusion are any real numbers, such as x = 0 and x = 5. If you substitute these values into the equation, you will get the same result on both sides.