The value of x in the solution set of the considered inequality is given by: Option A: -10
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.
For this case, we have:
[tex]3(x-4) \geq 5x+ 2\\[/tex]
Solving it,
[tex]3(x-4) \geq 5x+ 2\\\\\\3x - 12 \geq 5x + 2\\\\\text{Adding -3x -2 on both the sides}\\\\-12 -2 \geq 5x -3x\\-14 \geq 2x\\\\\text{Dividing both the sides by 2}\\\\\dfrac{-14}{2} \geq \dfrac{2x}{2}\\\\-7 \geq x\\\\x \leq -7[/tex]
Thus, the solution set for this inequality is all such values which are smaller or equal to -7.
Now, the no other value except -10 is in the solution set because [tex]-10 \leq -7[/tex]
Thus, the value of x in the solution set of the considered inequality is given by: Option A: -10
Learn more about solving inequalities here:
https://brainly.com/question/16339562
