-1.5x+>-1.375

1 answer

To solve the inequality \(-1.5x > -1.375\), follow these steps:

  1. Divide both sides by -1.5, remembering that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:

    \[ x < \frac{-1.375}{-1.5} \]

  2. Calculate the right hand side:

    \[ \frac{-1.375}{-1.5} = \frac{1.375}{1.5} \]

    To simplify \(\frac{1.375}{1.5}\):

    • Convert both to fractions: \(1.375 = \frac{11}{8}\) and \(1.5 = \frac{3}{2}\).
    • Then perform the division:

    \[ \frac{11/8}{3/2} = \frac{11}{8} \times \frac{2}{3} = \frac{11 \times 2}{8 \times 3} = \frac{22}{24} = \frac{11}{12} \]

  3. Final result: After simplifying, we find the solution to the inequality:

    \[ x < \frac{11}{12} \]

So the final answer is:

\[ x < \frac{11}{12} \]