Question

which number line shows the solution to this compound inequality? 0 ≤ -2x + 6 < 16

Explanation:

Step1: Solve left - hand side of inequality

Solve \(0\leq - 2x + 6\). Subtract 6 from both sides: \(0-6\leq - 2x+6 - 6\), which gives \(-6\leq - 2x\). Divide both sides by - 2 and reverse the inequality sign (since dividing by a negative number), we get \(3\geq x\) or \(x\leq3\).

Step2: Solve right - hand side of inequality

Solve \(-2x + 6<16\). Subtract 6 from both sides: \(-2x+6 - 6<16 - 6\), which gives \(-2x<10\). Divide both sides by - 2 and reverse the inequality sign, we get \(x>-5\).

Answer:

The solution of the compound inequality \(0\leq - 2x + 6<16\) is \(-5 < x\leq3\). This is represented by a number - line with an open circle at \(x = - 5\) (because \(x>-5\)) and a closed circle at \(x = 3\) (because \(x\leq3\)). So the answer is A.