What is the solution to this compound?
-6≤2x+6≤6
To find the solution to the compound inequality -6 ≤ 2x + 6 ≤ 6, we can start by subtracting 6 from all sides of the inequality:
-6 - 6 ≤ 2x + 6 - 6 ≤ 6 - 6
-12 ≤ 2x ≤ 0
Next, we divide all sides by 2 to isolate the x variable:
-12/2 ≤ 2x/2 ≤ 0/2
-6 ≤ x ≤ 0
Thus, the solution to the compound inequality is -6 ≤ x ≤ 0.
To find the solution to this compound inequality, we need to solve each inequality separately and then find the overlap between the solutions.
First, let's solve the left inequality:
-6 ≤ 2x + 6
Subtract 6 from both sides:
-6 - 6 ≤ 2x
-12 ≤ 2x
Divide both sides by 2:
-6 ≤ x
Now let's solve the right inequality:
2x + 6 ≤ 6
Subtract 6 from both sides:
2x ≤ 0
Divide both sides by 2:
x ≤ 0
Now, looking at both inequalities, we find the overlap between the solutions:
-6 ≤ x ≤ 0
So, the solution to the compound inequality is -6 ≤ x ≤ 0.
To find the solution to the compound inequality -6 ≤ 2x + 6 ≤ 6, we need to solve it step by step.
First, let's isolate the variable by subtracting 6 from all three parts of the compound inequality:
-6 - 6 ≤ 2x + 6 - 6 ≤ 6 - 6
-12 ≤ 2x ≤ 0
Now, divide all three parts of the compound inequality by 2 to solve for x:
-12/2 ≤ 2x/2 ≤ 0/2
-6 ≤ x ≤ 0
Therefore, the solution to the compound inequality -6 ≤ 2x + 6 ≤ 6 is x ∈ [-6, 0]. This means that x can take any value between -6 and 0 (including -6 and 0).