Answer
This inequality is true for every value of $x$; therefore, the solution is the set of all real numbers, or $(-∞, ∞)$.
Work Step by Step
To solve the inequality, we need to isolate variables on one side of the inequality and the constants on the other side.
First, let's use distributive property:
$$2(x) + 2(3) > 2x + 1$$
Multiply:
$$2x + 6 > 2x + 1$$
Subtract $2x$ from both sides of the inequality:
$$(2x - 2x) + 6 > (2x - 2x) + 1$$
The $2x$ terms cancel out on both sides of the inequality:
$$6 > 1$$
This inequality is true for every value of $x$; therefore, the solution is the set of all real numbers, or $(-∞, ∞)$.
