what are all integer values of x in the interval 5≤x<10 that satisfy the following inequality: -2x+1>-11
To solve the inequality, we need to isolate the variable x.
We start by subtracting 1 from both sides:
-2x + 1 - 1 > -11 - 1
-2x > -12
Next, we divide both sides by -2. Remember that when dividing by a negative number, the inequality sign flips:
(-2x) / -2 < -12 / -2
x < 6
Therefore, all the integer values of x in the interval 5≤x<10 that satisfy the inequality -2x + 1 > -11 are x = 5.
To find the integer values of x that satisfy the inequality -2x + 1 > -11, we need to solve the inequality:
-2x + 1 > -11
First, we can simplify the inequality by subtracting 1 from both sides:
-2x > -12
Next, divide both sides of the inequality by -2. Since we are dividing by a negative number, the direction of the inequality sign will flip:
x < -12/-2
Simplifying further, we have:
x < 6
Now, since we are looking for integer values of x in the interval 5 ≤ x < 10, we need to find the integers that are less than 6 within this interval. The integers that satisfy this condition are:
5
Therefore, the only integer value of x in the interval 5 ≤ x < 10 that satisfies the inequality -2x + 1 > -11 is x = 5.
To determine the integer values of x that satisfy the inequality -2x + 1 > -11 in the interval 5 ≤ x < 10, you can follow these steps:
Step 1: Solve the inequality.
-2x + 1 > -11
First, subtract 1 from both sides:
-2x > -12
Next, divide both sides by -2, remembering to reverse the inequality since we divided by a negative number:
x < (-12) / (-2)
x < 6
So, the solution to the inequality is x < 6.
Step 2: Identify the integer values of x in the given interval.
The given interval is 5 ≤ x < 10. This means x is greater than or equal to 5, but less than 10.
The integer values of x in this interval are:
5, 6, 7, 8, 9
So, the integer values of x that satisfy the inequality -2x + 1 > -11 in the interval 5 ≤ x < 10 are: 5, 6, 7, 8, 9.