Can anyone help me solve this problem; 2x + 3 = 2x + 4 - 1 and explain why there are an infinite number of solutions? Thanks!!
Can anyone show me a step-by-step on how to solve it, too? Thanks!
2x + 3 = 2x + 4 - 1
2x - 2x + 3 = 3
2x - 2x + 3 - 3 = 3 - 3
0 = 0
Thank you one again Ms. Sue! You're truly amazing. :)
*once
If , when solving an equation, the variable drops out and
1. you end up with a true statement, then there will be an infinite number of solutions, and your equation is an identity
e.g. see above
2. you end up with a false statement , then there will be no solution
e.g. 2x +3 = 2x + 5
3 = 5 , which is false
thus , no solution.
Thank you Reiny too.
To solve the equation 2x + 3 = 2x + 4 - 1, we start by simplifying each side of the equation.
On the left side, we have 2x + 3.
On the right side, we have 2x + 4 - 1, which simplifies to 2x + 3.
Now, we can see that both sides of the equation are exactly the same. So, the equation simplifies to:
2x + 3 = 2x + 3
At this point, we notice that the variable x is present on both sides of the equation. When we subtract 2x from both sides, it cancels out on both sides since the equation is balanced. This leaves us with:
3 = 3
The equation 3 = 3 is always true, no matter the value of x. So, we conclude that there are an infinite number of solutions to the given equation.
The reason why there are an infinite number of solutions is that when we simplified the equation, we found that both sides were identical. This indicates that any value of x will satisfy the equation, making it true. Therefore, there are infinite values of x that solve the equation.