Solve & Graph: 4 < -2x - 6 < 14

Answer

To solve the compound inequality 4 < -2x - 6 < 14, follow these steps: 1. Isolate the variable term by adding 6 to all three parts of the inequality: 4 + 6 < -2x - 6 + 6 < 14 + 6, which simplifies to 10 < -2x < 20. 2. Isolate x by dividing all three parts by -2. Remember that when dividing or multiplying an inequality by a negative number, you must reverse the inequality signs: 10 / -2 > -2x / -2 > 20 / -2, which simplifies to -5 > x > -10. 3. Rewrite the inequality in standard order from least to greatest: -10 < x < -5. This means x is between -10 and -5. To graph this on a number line, place open circles at -10 and -5 to indicate that these values are not included (because the signs are 'less than' and not 'less than or equal to'). Then, shade the horizontal line segment between these two circles.