To solve the inequality [tex]\(5x + 2 > 7x - 2x + 3\)[/tex], we'll follow these detailed steps:
1. Simplify the Inequality:
Combine like terms on the right-hand side of the inequality:
[tex]\[
7x - 2x = 5x
\][/tex]
So, the inequality simplifies to:
[tex]\[
5x + 2 > 5x + 3
\][/tex]
2. Isolate the Variable:
To isolate the variable [tex]\(x\)[/tex], we subtract [tex]\(5x\)[/tex] from both sides of the inequality:
[tex]\[
5x + 2 - 5x > 5x + 3 - 5x
\][/tex]
This simplifies to:
[tex]\[
2 > 3
\][/tex]
3. Analyze the Simplified Inequality:
We end up with [tex]\(2 > 3\)[/tex].
4. Interpreting the Result:
The statement [tex]\(2 > 3\)[/tex] is false. Since this inequality does not hold true, it indicates that there is no value of [tex]\(x\)[/tex] that can satisfy the initial inequality. Hence, the solution to the inequality is:
[tex]\[
\boxed{\text{False}}
\][/tex]
