For the equation w + 10 = w + 9, can you substitute a value for w to make this a true number sentence? Make sure to explain your answer.
No, it is not possible to substitute a value for w to make the equation w + 10 = w + 9 a true number sentence.
This is because in the equation, w appears on both sides of the equation with different coefficients. No matter what value we substitute for w, the equation is always false.
Let's try substituting a value to demonstrate:
If we substitute w = 1, we have:
1 + 10 = 1 + 9
11 = 10
As we can see, the equation is not true. The left side of the equation is 11 while the right side is 10.
This shows that there is no value we can substitute for w to make the equation w + 10 = w + 9 true.
To determine if you can substitute a value for w to make the equation w + 10 = w + 9 a true number sentence, we need to simplify the equation and solve for w.
Let's start by subtracting w from both sides of the equation to eliminate the variable terms on one side:
w + 10 - w = w + 9 - w
Simplifying this further, we get:
10 = 9
Now, if we compare 10 with 9, we can see that they are not equal. Therefore, there is no value of w that we can substitute to make this equation a true number sentence.
In this case, no matter what value we assign to w, the equation will always be false, as it violates the fundamental principle of mathematics that states that the left side of the equation must be equal to the right side.
Therefore, the equation w + 10 = w + 9 has no solutions, and we cannot substitute any value for w to make it a true number sentence.
To determine if there is a value for w that makes the equation w + 10 = w + 9 true, we can start by simplifying the equation.
Given: w + 10 = w + 9
We can subtract w from both sides of the equation, which results in:
10 = 9
By subtracting w from both sides, the variables cancel out, leaving us with a constant on both sides of the equation. In this case, 10 is not equal to 9, so the equation 10 = 9 is false.
Therefore, no matter what value we substitute for w, the equation w + 10 = w + 9 will never be true.