Use the inequality to answer Parts 1-3.

Question

-3(x-2)equal to or greater than 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.

Answer 1

To solve the inequality -3(x-2) ≥ 1/3, we can start by distributing the -3 to the terms inside the parentheses:

-3x + 6 ≥ 1/3

Next, we can subtract 6 from both sides to isolate the variable:

-3x ≥ 1/3 - 6

-3x ≥ -17/3

To get rid of the coefficient (-3) in front of x, we can divide both sides by -3. However, whenever we divide an inequality by a negative number, we must switch the direction of the inequality symbol. So, dividing both sides by -3 gives us:

x ≤ 17/9

Part 1: The solution to the inequality is x ≤ 17/9.

Part 2: The verbal statement describing the solution is "x is less than or equal to seventeen ninths."

Part 3: To verify the solution, we can substitute two elements of the solution set into the original inequality and see if they satisfy it. Let's choose x = 1 and x = 17/9 as our test values:

For x = 1:
-3(1-2) ≥ 1/3
-3(-1) ≥ 1/3
3 ≥ 1/3
This is true since 3 is indeed greater than or equal to 1/3.

For x = 17/9:
-3(17/9 - 2) ≥ 1/3
-3(17/9 - 18/9) ≥ 1/3
-3(-1/9) ≥ 1/3
1/3 ≥ 1/3
This is also true since 1/3 is equal to 1/3.

Both test values satisfy the original inequality, confirming that our solution x ≤ 17/9 is correct.