Subjects algebra

Distance Difference

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1. **State the problem:** A student bikes distances given by expressions on Monday and Tuesday: Monday's distance is $5t + 4$ km and Tuesday's distance is $3t + 2$ km. We need to find how much farther the student biked on Monday compared to Tuesday. 2. **Formula used:** To find how much farther on Monday, subtract Tuesday's distance from Monday's distance: $$\text{Difference} = (5t + 4) - (3t + 2)$$ 3. **Simplify the expression:** $$\text{Difference} = 5t + 4 - 3t - 2$$ Combine like terms: $$\text{Difference} = (5t - 3t) + (4 - 2) = 2t + 2$$ 4. **Interpretation:** The student biked $2t + 2$ km farther on Monday than on Tuesday. 5. **Answer choice:** Among the options given, $2t + 2$ matches our result. **Final answer:** $2t + 2$