Which values are in the solution set of the inequality - 2/3 * x + 13 >= - 1 ?
Select all that apply.
O 19
O 20
O 21
O 22
O 23
To find the solution set of the inequality, we need to isolate the variable x.
-2/3 * x + 13 >= -1
First, we can subtract 13 from both sides:
-2/3 * x >= -1 - 13
-2/3 * x >= -14
Next, we can multiply both sides by -3/2 (or divide by -2/3, which is the same thing) to solve for x:
-2/3 * x * -3/2 <= -14 * -3/2
x <= 21
Therefore, the values in the solution set are 21 or any value less than or equal to 21.
So, the correct answer choices are:
- 19
- 20
- 21
To solve the inequality, we need to isolate the variable x.
-2/3 * x + 13 >= -1
First, let's subtract 13 from both sides of the inequality to move the constant term to the other side.
-2/3 * x >= -14
Next, let's multiply both sides of the inequality by -3/2 to cancel out the coefficient of x and reverse the inequality sign since we are multiplying by a negative number.
x <= (-14) * (-3/2)
x <= 21
So, the solution to the inequality is x ≤ 21.
Therefore, the values in the solution set of the inequality are 19, 20, and 21.
The correct options are:
- 19
- 20
- 21
To find the values that are in the solution set of the inequality -2/3 * x + 13 >= -1, we need to solve the inequality. Here's how to do it:
Step 1: Subtract 13 from both sides of the inequality:
-2/3 * x + 13 - 13 >= -1 - 13
-2/3 * x >= -14
Step 2: Multiply both sides of the inequality by -3/2. Remember that when we multiply or divide an inequality by a negative number, we need to flip the direction of the inequality sign.
(-2/3 * x) * (-3/2) <= (-14) * (-3/2)
x <= 21
So the solution to the inequality is x <= 21.
Now let's check which values from the options are in the solution set.
Option 19:
Is 19 less than or equal to 21? Yes. This value is within the solution set.
Option 20:
Is 20 less than or equal to 21? Yes. This value is within the solution set.
Option 21:
Is 21 less than or equal to 21? Yes. This value is within the solution set.
Option 22:
Is 22 less than or equal to 21? No. This value is not within the solution set.
Option 23:
Is 23 less than or equal to 21? No. This value is not within the solution set.
Therefore, the values in the solution set of the inequality are 19, 20, and 21.