"Live in hope" is a commonly used phrase that expresses optimism about the future. The word "hope" itself can be replaced with other synonyms to convey the same sentiment. For example, instead of "live in hope," one can use "hold onto faith," "keep the faith," "cling to optimism," or "persevere with positivity." These alternative phrases signify that despite hardships or setbacks, one continues to believe in a positive outcome for the future. By using these synonyms, one can add variety and color to their language and express hope and positivity in a more nuanced way.