Respuesta :
The solution of the inequality 2(4x - 3) ≥ -3(3x) + 5x is true for all x such that its a real number bigger or equal to 0.5 (Option A: x ≥ 0.5)
What is a solution set to an inequality or an equation?
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
The considered inequality is:
[tex]2(4x - 3) \geq -3(3x) + 5x[/tex]
Simplifying its both sides, we get:
[tex]2(4x - 3) \geq -3(3x) + 5x\\8x-6\geq -9x + 5x\\8x-6 \geq -4x[/tex]
Adding 4x on both the sides, we get:
[tex]8x-6+4x \geq -4x + 4x\\(8+4)x - 6 \geq 0\\12x -6 \geq 0\\[/tex]
Adding 6 on both the sides, and dividing by 12, we get:
[tex]12x-6 +6 \geq 0+6\\12x \geq 6\\12x/12 \geq 6/12\\x \geq 0.5[/tex]
(some operations like addition, subtraction, multiplication by positive real number or division by positive real number keeps the inequality relation unaltered. With the use of such operations, here we tried to get x on one side, and constants on other side).
Thus, the considered inequality is true for all the values of x which are real numbers bigger or equal to 0.5 (Option A: x ≥ 0.5)
Learn more about inequalities here:
https://brainly.com/question/16339562
