Questions: Solve the compound inequality: (6 leq 2 x-8<14). Enter the exact answer in interval notation. To enter ∞, type infinity. To enter ∪, type U.

Solution Steps

The given compound inequality is \(6 \leq 2x - 8 < 14\). We can separate this into two simpler inequalities:

1. \(6 \leq 2x - 8\)
2. \(2x - 8 < 14\)

To solve \(6 \leq 2x - 8\), we first add 8 to both sides: \[ 6 + 8 \leq 2x \implies 14 \leq 2x \] Next, divide both sides by 2: \[ \frac{14}{2} \leq x \implies 7 \leq x \]

To solve \(2x - 8 < 14\), we add 8 to both sides: \[ 2x - 8 + 8 < 14 + 8 \implies 2x < 22 \] Next, divide both sides by 2: \[ x < \frac{22}{2} \implies x < 11 \]

The solutions to the inequalities are:

• \(x \geq 7\) from the first inequality
• \(x < 11\) from the second inequality

The intersection of these solutions is: \[ 7 \leq x < 11 \]

Final Answer