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

Since this is a three part inequality we must do the same thing to all three parts.Adding 8 to all three parts gives $LaTeX: \displaystyle -19 \leq 7 x - 8 < -15$ . Dividing off the coefficient of $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle - \frac{19}{7} \leq x < - \frac{15}{7}$ The solution is $LaTeX: \displaystyle \big[- \frac{19}{7},- \frac{15}{7}\big)$