-3(x - 2) -1 > 2 - 5(x -6)
-3x+6-1>2-5x+30
-3x+5>-5x+32
-3x>-5x+27
2x>27
x>27/2
To solve the inequality -3(x - 2) - 1 > 2 - 5(x - 6), we need to simplify the expression and isolate the variable on one side of the inequality symbol.
First, we'll start by distributing the terms inside the parentheses:
-3(x - 2) - 1 > 2 - 5(x - 6)
-3x + 6 - 1 > 2 - 5x + 30
Simplifying further:
-3x + 5 > 32 - 5x
Next, we want to isolate the variable terms and the constant terms on opposite sides of the inequality symbol. To do this, we will move the variable terms to the left side and the constant terms to the right side.
To move -5x to the left side, we need to add 5x to both sides:
-3x + 5 + 5x > 32 - 5x + 5x
2x + 5 > 32
Next, let's move the constant term (5) to the right side by subtracting 5 from both sides:
2x + 5 - 5 > 32 - 5
2x > 27
To solve for x, we need to eliminate the coefficient in front of x. To do this, we divide both sides of the inequality by the coefficient (2):
(2x)/2 > 27/2
x > 13.5
So, the solution to the inequality -3(x - 2) - 1 > 2 - 5(x - 6) is x > 13.5.
To check if this solution is correct, substitute any value greater than 13.5 into the original inequality and see if it holds true.