Solve the inequality $LaTeX: \displaystyle 0 \leq - 4 x - 9 < 13$ . Write the solution in interval notation.

Since this is a three part inequality we must do the same thing to all three parts.Adding 9 to all three parts gives $LaTeX: \displaystyle -9 \leq - 4 x - 9 < 4$ . Dividing off the coefficient of $LaTeX: \displaystyle x$ gives and reversing all of the inequalies $LaTeX: \displaystyle \frac{9}{4} \geq x > -1$ The solution is $LaTeX: \displaystyle \big(-1,\frac{9}{4}\big]$