Question

Solve the inequality 14x + 9 ≤ 2x - 5 < 34x + 10. Fill in the blanks to complete the solution set. ≤ x < question 2. Graph the solution set using the items below the number line. To place an item on the number line, click on the item, then click the location on the number line where you want to place the item. Drag one side to adjust if necessary.

Answer 1

To solve the inequality 14x + 9 ≤ 2x - 5 < 34x + 10, subtract 2x from all terms, then subtract 9 from all terms, and finally subtract 32x from all terms. Divide by -20 and simplify to get x ≥ 7/10 and x < -1/20.

Step-by-step explanation:

To solve the inequality 14x + 9 ≤ 2x - 5 < 34x + 10, we first subtract 2x from all the terms: 14x + 9 - 2x ≤ -5 < 34x + 10 - 2x. This gives us 12x + 9 ≤ -5 < 32x + 10. Then, we subtract 9 from all the terms: 12x + 9 - 9 ≤ -5 - 9 < 32x + 10 - 9. Simplifying further, we have 12x ≤ -14 < 32x + 1. Finally, we subtract 32x from all the terms: 12x - 32x ≤ -14 - 32x < 32x + 1 - 32x. This simplifies to -20x ≤ -14 < 1. To get the solution set, we divide by -20, giving us -20x/-20 ≥ -14/-20 < 1/-20. Since we are dividing by a negative number, the inequality sign flips. So, we have x ≥ 14/20 (which simplifies to x ≥ 7/10) and x < -1/20.