Find the solution set to the inequality, express the solution in set notation 4 (x + 3) greater than or equal to 2 (2x - 2) Show your work in vertical form
4(x + 3) ≥ 2(2x - 2)
Distribute on the left side:
4x + 12 ≥ 4x - 4
Subtract 4x from both sides:
12 ≥ -4
Since 12 is greater than -4, this inequality is true for all values of x.
The solution set in set notation is (-∞, ∞).
To solve the inequality:
4(x + 3) ≥ 2(2x - 2)
First, distribute the 4 and 2 on the left and right sides of the inequality, respectively:
4x + 12 ≥ 4x - 4
Next, subtract 4x from both sides to isolate the variable:
4x - 4x + 12 ≥ 4x - 4x - 4
Simplifying further:
12 ≥ -4
Since 12 is greater than -4, the inequality is true for all values of x. This means the solution set is all real numbers.
Expressing this in set notation, the solution is:
{x | x ∈ ℝ}
To solve the inequality 4(x + 3) ≥ 2(2x - 2), we need to distribute the coefficients and simplify the expression.
Let's start by distributing the coefficients:
4(x + 3) ≥ 2(2x - 2)
4x + 12 ≥ 4x - 4
Next, we can cancel out the 4x terms on both sides of the inequality:
4x + 12 - 4x ≥ 4x - 4 - 4x
12 ≥ -4
Since 12 is greater than or equal to -4, the inequality is true for all values of x.
The solution set to the inequality is the set of all real numbers: (-∞, +∞) or simply ℝ (the set of real numbers).