To solve the equation [tex]\(7 + 5 + 3 + x = x + 19 - 3\)[/tex], let's break it down step-by-step:
1. Combine like terms on each side of the equation:
[tex]\[
7 + 5 + 3 + x \quad \text{and} \quad x + 19 - 3
\][/tex]
2. Simplify the left side:
[tex]\[
(7 + 5 + 3) + x = 15 + x
\][/tex]
3. Simplify the right side:
[tex]\[
x + (19 - 3) = x + 16
\][/tex]
4. Now our equation looks like this:
[tex]\[
15 + x = x + 16
\][/tex]
5. Subtract [tex]\(x\)[/tex] from both sides to isolate the constants:
[tex]\[
15 + x - x = x + 16 - x \implies 15 = 16
\][/tex]
6. At this step, we see we have a contradiction:
[tex]\[
15 = 16
\][/tex]
Since [tex]\(15\)[/tex] can never equal [tex]\(16\)[/tex], this contradiction tells us that there is no value of [tex]\(x\)[/tex] that would make the original equation true.
Therefore, there is no solution to the equation [tex]\(7 + 5 + 3 + x = x + 19 - 3\)[/tex].
