Final answer:
To solve the absolute value inequality |4x+5| < 14, break it into two separate inequalities: 4x+5 < 14 and -(4x+5) < 14. The solution is -4.75 < x < 2.25.
Step-by-step explanation:
To solve the absolute value inequality |4x+5| < 14, we can break it into two separate inequalities: 4x+5 < 14 and -(4x+5) < 14.
- For the first inequality, 4x+5 < 14, we subtract 5 from both sides to get 4x < 9. Then, we divide both sides by 4 to find that x < 9/4 or x < 2.25.
- For the second inequality, -(4x+5) < 14, we distribute the negative sign to get -4x-5 < 14. Then, we add 5 to both sides to get -4x < 19. Finally, we divide both sides by -4, remembering to reverse the inequality sign because we are dividing by a negative number, and we find x > -19/4 or x > -4.75.
Therefore, the solution to the absolute value inequality |4x+5| < 14 is -4.75 < x < 2.25.