Solve
-8≤2x-4<2
To solve the inequality, we will solve each part of it individually.
Starting with -8 ≤ 2x - 4:
Add 4 to both sides:
-8 + 4 ≤ 2x - 4 + 4
-4 ≤ 2x
Divide both sides by 2 (since we are dividing by a positive number, we don't need to switch the inequality sign):
-4/2 ≤ 2x/2
-2 ≤ x
Now let's solve the second part of the inequality: 2x - 4 < 2:
Add 4 to both sides:
2x - 4 + 4 < 2 + 4
2x < 6
Divide both sides by 2:
(2/2)x < 6/2
x < 3
So the solution to the inequality is:
-2 ≤ x < 3
To solve the inequality -8 ≤ 2x - 4 < 2, we will break it down into two separate inequalities and find the solution set for each one.
First, let's solve the left inequality, -8 ≤ 2x - 4:
-8 ≤ 2x - 4
Adding 4 to both sides:
-8 + 4 ≤ 2x - 4 + 4
Simplifying:
-4 ≤ 2x
Next, divide both sides by 2:
-4/2 ≤ 2x/2
Simplifying further:
-2 ≤ x
So, the solution to the left inequality is x ≥ -2.
Now, let's solve the right inequality, 2x - 4 < 2:
2x - 4 < 2
Adding 4 to both sides:
2x - 4 + 4 < 2 + 4
Simplifying:
2x < 6
Next, divide both sides by 2:
(2/2)x < 6/2
Simplifying further:
x < 3
So, the solution to the right inequality is x < 3.
Combining the solutions for both inequalities, we find that the overall solution to the original inequality -8 ≤ 2x - 4 < 2 is -2 ≤ x < 3.
To solve the inequality -8 ≤ 2x - 4 < 2, we need to determine the range of values that x can take.
Let's start by solving the first part of the inequality, -8 ≤ 2x - 4.
-8 ≤ 2x - 4
Add 4 to both sides:
-8 + 4 ≤ 2x
-4 ≤ 2x
Divide both sides by 2 (since we are trying to isolate x):
-2 ≤ x
So the first part of the inequality becomes: -2 ≤ x.
Now let's solve the second part of the inequality, 2x - 4 < 2.
2x - 4 < 2
Add 4 to both sides:
2x < 6
Divide both sides by 2:
x < 3
So the second part of the inequality becomes: x < 3.
Now, we need to find the intersection of these two inequalities to determine the values of x that satisfy both conditions.
Taking the common interval between -2 ≤ x and x < 3, we find that the solution to the inequality is:
-2 ≤ x < 3.
To summarize, the values of x that satisfy the inequality -8 ≤ 2x - 4 < 2 are -2 or any value greater than or equal to -2 to less than 3.