Solve the inequality $LaTeX: \displaystyle 1 \leq 8 - 2 x < 6$ . Write the solution in interval notation.

Since this is a three part inequality we must do the same thing to all three parts.Subtracting 8 from all three parts gives $LaTeX: \displaystyle -7 \leq 8 - 2 x < -2$ . Dividing off the coefficient of $LaTeX: \displaystyle x$ gives and reversing all of the inequalies $LaTeX: \displaystyle \frac{7}{2} \geq x > 1$ The solution is $LaTeX: \displaystyle \big(1,\frac{7}{2}\big]$