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
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:
$\boxed{(-\infty, +\infty)}$
I do not have dollar signs in my original equation. Please redo without the dollar signs.
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:
(-∞, +∞)
To solve the inequality 4(x + 3) > 2(2x - 2), we can distribute and simplify both sides:
4(x + 3) > 2(2x - 2)
4x + 12 > 4x - 4
Next, we can simplify the equation by subtracting 4x from both sides:
4x + 12 - 4x > 4x - 4 - 4x
12 > -4
Since 12 is always greater than -4, the inequality is true for all values of x. Therefore, the solution set is all real numbers.
Expressing this solution in set notation, we have:
{x | x is a real number}
To find the solution set to the inequality 4(x + 3) > 2(2x - 2), we will solve it step by step:
Step 1: Distribute the coefficients:
4x + 12 > 4x - 4
Step 2: Simplify the equation:
As we can observe, the term "4x" appears on both sides. To simplify the equation further, we can subtract 4x from both sides:
4x - 4x + 12 > 4x - 4x - 4
12 > -4
Step 3: Since 12 is always greater than -4, the inequality holds true for all values of x. Thus, the solution set is the set of all real numbers, which can be expressed as (-∞, +∞) in set notation.
Therefore, the solution set to the inequality 4(x + 3) > 2(2x - 2) is (-∞, +∞).