Find the solution set to the inequality, express the solution in set notation 4(x + 3) > 2 (2x - 2) Show your work in vertical form

Answer 1

To solve the inequality $4(x + 3) > 2 (2x - 2)$:

First, distribute on both sides of the inequality:
$4x + 12 > 4x - 4$

Next, subtract $4x$ from both sides of the inequality:
$12 > -4$

This is a true statement ($12$ is indeed greater than $-4$), which means that the inequality is satisfied for all values of $x$.

Therefore, the solution to the inequality is the set of all real numbers, or in set notation:

$\boxed{(-\infty, +\infty)}$

Answer 2

I do not have dollar signs in my original equation. Please redo without the dollar signs.

Answer 3

Certainly! Here is the solution without the use of dollar signs:

To solve the inequality 4(x + 3) > 2 (2x - 2):

First, distribute on both sides of the inequality:
4x + 12 > 4x - 4

Next, subtract 4x from both sides of the inequality:
12 > -4

This is a true statement (12 is indeed greater than -4), which means that the inequality is satisfied for all values of x.

Therefore, the solution to the inequality is the set of all real numbers, or in set notation:

(-∞, +∞)