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
To determine the number of solutions for the equation 2(x+3)=2x+6, let's simplify and solve it step by step:
First, distribute the 2 to both terms inside the parentheses:
2*x + 2*3 = 2x + 6
2x + 6 = 2x + 6
Next, we can subtract 2x from both sides to eliminate the variable terms:
2x - 2x + 6 = 2x - 2x + 6
6 = 6
Since 6 is equal to 6, the equation is true for every value of x. Therefore, it has an infinite number of solutions.
To support this conclusion, we can provide any two values for x as examples. For instance, if we choose x = 1 and x = 2, we will find:
When x = 1:
2(1+3) = 2*1 + 6
2(4) = 2 + 6
8 = 8
When x = 2:
2(2+3) = 2*2 + 6
2(5) = 4 + 6
10 = 10
Both of these examples satisfy the equation, confirming that there are an infinite number of solutions.