Ok, so when you are solving an equation, and you have an answer such as
5x=0 , does that mean that it is no solution or all real #s?
And, when the answer is
4=4 , does that mean it is no solution or all real #s?
And when the answer is
2x=2x, does that mean it is no solution or all real #s?
Thank you
For 5x=0, x=0 because when you divide 0 by 5; it is x=0. The second one would be "All Real Numbers". The 3rd one would be "No solution".
When you solve an equation and end up with an identity like 5x = 0, where 0 is on one side of the equation and a variable (x) is on the other side, it means that the equation is true for all real values of x. In this case, you can divide both sides of the equation by 5 to isolate the variable: x = 0. Since any value multiplied by 0 equals 0, the equation holds true for any real number.
Similarly, when you have an equation like 4 = 4, it means that both sides of the equation are equal. In this case, the equation is true for all real numbers because any number is always equal to itself. This equation has infinitely many solutions.
Lastly, when you have an equation like 2x = 2x, where the same variable is present on both sides of the equation, it also means that the equation is true for all real values of x. In this case, you can divide both sides of the equation by 2x (assuming x is not equal to zero) to simplify it to 1 = 1. Again, this equation holds true for any value of x as it is an identity.
Therefore, the equations 5x = 0, 4 = 4, and 2x = 2x all have all real numbers as their solutions.