Answer
The inequality will be satisfied for all real number values of x
Work Step by Step
We are given that $2(x+3)\gt2x+1$
We can solve for x by using the distributive property to simplify the left side.
$2x+6\gt2x+1$
Subtract 1 from both sides.
$2x+5\gt2x$
Subtract 2x from both sides.
$5\gt0$
This is true for all values of x, so the inequality is satisfied for all real numbers.