Solve 12x-25¡Ý3x-5(x+6) using set builder notation
To solve the inequality 12x - 25 ≥ 3x - 5(x + 6), we first simplify the equation and then express the solution using set builder notation.
Let's simplify the inequality step by step:
12x - 25 ≥ 3x - 5x - 30
12x - 25 ≥ -2x - 30
Next, we want to isolate the variable x on one side of the inequality sign. To do this, we'll add 2x to both sides:
12x + 2x - 25 ≥ -2x + 2x - 30
14x - 25 ≥ -30
Now, we can simplify further by adding 25 to both sides:
14x - 25 + 25 ≥ -30 + 25
14x ≥ -5
Finally, divide both sides by 14 to obtain the solution:
x ≥ -5/14
Using set builder notation, we can express the solution as:
{x | x ≥ -5/14}
This notation reads as "the set of all x such that x is greater than or equal to -5/14".