Respuesta :
The inequality describes the possible values of the variable x as being
larger than [tex]1\frac{8}{9}[/tex]
Part 1:
[tex]x \geq \underline{1\frac{8}{9}}[/tex]
Part 2: x is the set of all real numbers greater than [tex]\underline{1\frac{8}{9}}[/tex]
Part 3: The solution set includes 2, and 3
By testing, we have;
When x = 2; -3×(2 - 2) = 0 ≤ 1/3;
When x = 3; -3 × (3 - 2) = -3 ≤ 1/3
How to find the solution and test the inequality?
The given inequality is -3·(x - 2) ≤ 1/3
Part 1:
The solution of the inequality can be found by making x the subject of the inequality as follows;
-3·(x - 2) ≤ 1/3
[tex](x - 2) \geq \dfrac{1}{3 \times (-3)} = -\dfrac{1}{9}[/tex]
- [tex]x \geq -\dfrac{1}{9} + 2 = \dfrac{17}{9} = 1\frac{8}{9}[/tex]
[tex]x \geq \underline{1\frac{8}{9}}[/tex]
Part 2: The verbal statement describing the solution of the inequality is as follows;
- The solution of the inequality is that the value of x is the set of all real numbers greater than [tex]\underline{1\frac{8}{9}}[/tex]
Part 3: The elements of the solution set which are numbers greater than [tex]1\frac{8}{9}[/tex] include 2, and 3
By testing, we have;
When x = 2; -3×(2 - 2) = 0 ≤ 1/3;
When x = 3, we have;
-3 × (3 - 2) = -3 ≤ 1/3
Learn more about inequalities here:
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