Which of the following values are solutions to the inequality minus, 2, is less than or equal to, 9, minus, 4, x, question mark−2≤9−4x?
I., 10, II., minus, 4, III., 6
I.10II.−4III.6
To determine which values are solutions to the inequality, we substitute the values into the inequality and see if the inequality holds true.
I. Substitute 10 into the inequality: -2 ≤ 9 - 4(10)
-2 ≤ 9 - 40
-2 ≤ -31
This inequality is not true, so 10 is not a solution to the inequality.
II. Substitute -4 into the inequality: -2 ≤ 9 - 4(-4)
-2 ≤ 9 + 16
-2 ≤ 25
This inequality is true, so -4 is a solution to the inequality.
III. Substitute 6 into the inequality: -2 ≤ 9 - 4(6)
-2 ≤ 9 - 24
-2 ≤ -15
This inequality is not true, so 6 is not a solution to the inequality.
The correct answers are: II. -4
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-5
0
5
-1
Select the values that make the inequality t, is greater than, minus, 1t>−1 true.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2
-9 -6 -4
-2 -1.1 -1.01
-1.001 -1 -0.999
-0.99 -0.9 0
2 4 7
To determine which values make the inequality t > -1 true, we substitute each value into the inequality and see if the inequality holds true.
-5 > -1: This inequality is true.
0 > -1: This inequality is true.
5 > -1: This inequality is true.
-1 > -1: This inequality is not true.
Therefore, the values that make the inequality t > -1 true are -5, 0, and 5.
The correct answer is: -5, 0, 5
no out of these what makes t>-1 true
-9 -6 -4
-2 -1.1 -1.01
-1.001 -1 -0.999
-0.99 -0.9 0
2 4 7
To determine which values make the inequality t > -1 true, we can simply look at the given numbers and identify the values that are greater than -1.
From the given numbers, the following values are greater than -1:
-9
-6
-4
-2
-0.99
-0.9
0
2
4
7
Therefore, the values that make the inequality t > -1 true are:
-9, -6, -4, -2, -0.99, -0.9, 0, 2, 4, 7.
its wrong
I apologize for the incorrect response.
Let's go through the values one by one to determine which ones make the inequality t > -1 true.
-9 > -1: This inequality is false.
-6 > -1: This inequality is false.
-4 > -1: This inequality is false.
-2 > -1: This inequality is false.
-1.1 > -1: This inequality is true.
-1.01 > -1: This inequality is true.
-1.001 > -1: This inequality is true.
-0.99 > -1: This inequality is true.
-0.9 > -1: This inequality is true.
0 > -1: This inequality is true.
2 > -1: This inequality is true.
4 > -1: This inequality is true.
7 > -1: This inequality is true.
Based on the analysis, the values that make the inequality t > -1 true are:
-1.1, -1.01, -1.001, -0.99, -0.9, 0, 2, 4, 7.
To find the solutions to the given inequality, we need to solve the equation and determine the values of x that satisfy it.
The given inequality is: -2 ≤ 9 - 4x
To isolate the variable x, we can start by subtracting 9 from both sides of the inequality:
-2 - 9 ≤ 9 - 4x - 9
Simplifying the equation:
-11 ≤ -4x
Next, we divide both sides of the inequality by -4. Since we are dividing by a negative number, it's important to remember that when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.
(-11)/(-4) ≥ (-4x)/(-4)
Simplifying:
11/4 ≥ x
Therefore, the inequality is satisfied when x is less than or equal to 11/4.
Now, we can check the given values to see which ones satisfy the inequality:
I. 10: We substitute x = 10 into the inequality: -2 ≤ 9 - 4(10)
-2 ≤ 9 - 40
-2 ≤ -31
This is false, so 10 is not a solution.
II. -4: We substitute x = -4 into the inequality: -2 ≤ 9 - 4(-4)
-2 ≤ 9 + 16
-2 ≤ 25
This is true, so -4 is a solution.
III. 6: We substitute x = 6 into the inequality: -2 ≤ 9 - 4(6)
-2 ≤ 9 - 24
-2 ≤ -15
This is false, so 6 is not a solution.
Therefore, the only solution to the inequality is x = -4 (choice II).