Which of the following values are solutions to the inequality minus, 6, minus, x, is less than or equal to, 7, question mark−6−x≤7?
I., minus, 13, II., minus, 14, III., minus, 6
.−13 .−14 .−6
To solve the inequality, we can start by subtracting -6 from both sides:
-6 - x <= 7 - 6
-x <= 1
Next, we want to isolate x by multiplying both sides by -1. However, when we multiply or divide an inequality by a negative number, we need to reverse the inequality sign. So we have:
x >= -1
This means that any value of x that is greater than or equal to -1 will satisfy the inequality. So, -13, -14, and -6 are all solutions to the inequality.
To solve the inequality -6 - x ≤ 7, we will isolate the variable x.
First, we can move the -6 to the other side by adding 6 to both sides of the inequality:
-6 - x + 6 ≤ 7 + 6
This simplifies to:
-x ≤ 13
Next, we can multiply both sides by -1 (remember that whenever we multiply both sides of an inequality by a negative number, the direction of the inequality sign switches):
x ≥ -13
Therefore, x is greater than or equal to -13.
Now, let's determine which of the given values (-13, -14, -6) satisfies this inequality:
-13 ≥ -13 (True)
-14 ≥ -13 (False)
-6 ≥ -13 (True)
From the given values, only -13 and -6 serve as solutions to the inequality.
To check which values are solutions to the inequality -6 - x ≤ 7, we need to substitute each value into the inequality and see if the inequality holds true.
For option I, we substitute -13 into the inequality:
-6 - (-13) ≤ 7
Simplifying the expression within the inequality:
-6 + 13 ≤ 7
7 ≤ 7
Since 7 is equal to 7, option I is a solution to the inequality.
For option II, we substitute -14 into the inequality:
-6 - (-14) ≤ 7
Simplifying the expression within the inequality:
-6 + 14 ≤ 7
8 ≤ 7
Since 8 is not less than or equal to 7, option II is not a solution to the inequality.
For option III, we substitute -6 into the inequality:
-6 - (-6) ≤ 7
Simplifying the expression within the inequality:
-6 + 6 ≤ 7
0 ≤ 7
Since 0 is less than or equal to 7, option III is a solution to the inequality.
Therefore, the values that are solutions to the inequality are -13 and -6 (options I and III). Option II, which is -14, is not a solution.