contestada

Use the inequality to answer Parts 1-3.
−3(x−2)≤1/3
Part 1: Solve the inequality. Leave answer in terms of a whole number or reduced improper fraction.
Part 2: Write a verbal statement describing the solution to the inequality.
Part 3: Verify your solution to the inequality using two elements of the solution set.

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:

https://brainly.com/question/5183393

Otras preguntas