Certainly! Let's solve the equation step-by-step.
### Given:
[tex]\[ \sqrt{2} - 3 + 3 = x + 1 \][/tex]
1. Simplify the left-hand side of the equation:
[tex]\[ \sqrt{2} - 3 + 3 \][/tex]
Since [tex]\(-3 + 3\)[/tex] equals [tex]\(0\)[/tex], we can simplify this to:
[tex]\[ \sqrt{2} \][/tex]
So the equation now looks like:
[tex]\[ \sqrt{2} = x + 1 \][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], subtract [tex]\(1\)[/tex] from both sides of the equation:
[tex]\[ \sqrt{2} - 1 = x \][/tex]
or equivalently,
[tex]\[ x = \sqrt{2} - 1 \][/tex]
### Solution:
The equation [tex]\( \sqrt{2} - 3 + 3 = x + 1 \)[/tex] simplifies to [tex]\( \sqrt{2} = x + 1 \)[/tex]. After solving for [tex]\(x\)[/tex], we find:
[tex]\[ x = -1 + \sqrt{2} \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = -1 + \sqrt{2} \][/tex]
