The correct answer is: D.
The solution to the compound inequality 0 ≤ -2x + 6 < 16, we can solve each part separately:
Solve 0 ≤ -2x + 6:
Start with the inequality 0 ≤ -2x + 6
Add 2x to both sides: 2x ≤ 6
Divide by 2 (since the coefficient of x is -2) and reverse the inequality sign: x ≥ 3
Solve -2x + 6 < 16:
Start with the inequality -2x + 6 < 16
Subtract 6 from both sides: -2x < 10
Divide by -2 (and reverse the inequality sign): x > -5
Combine the two inequalities: x ≥ 3 and x > -5
The solution to the compound inequality is x > 3
Now, let's analyze the options:
A) (-5, 3] - This represents numbers between -5 and 3, including -5 but excluding 3. This is not the correct answer.
B) -[5, 3) - This represents numbers between -5 and 3, excluding both -5 and 3. This is not the correct answer.
C) [-5, 3) - This represents numbers between -5 and 3, including -5 but excluding 3. This is not the correct answer.
D) (-5, 3) - This represents numbers between -5 and 3, excluding both -5 and 3. This is the correct answer.
Therefore, the correct answer is D) number line has -14 to 10 is (-5, 3).