Solve the inequality $LaTeX: \displaystyle -7 \leq 3 - 8 x < 11$ . Write the solution in interval notation.

Since this is a three part inequality we must do the same thing to all three parts.Subtracting 3 from all three parts gives $LaTeX: \displaystyle -10 \leq 3 - 8 x < 8$ . Dividing off the coefficient of $LaTeX: \displaystyle x$ gives and reversing all of the inequalies $LaTeX: \displaystyle \frac{5}{4} \geq x > -1$ The solution is $LaTeX: \displaystyle \big(-1,\frac{5}{4}\big]$