Subjects algebra

Exam Inequality Fraction

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Exam Inequality Fraction


1. Problem 16: A student scores 10 out of 15 on Part 1 and 4 out of 10 on Part 2. To pass the exam, the student needs at least 54% of the total marks. 2. Calculate total marks obtained by the student: $$\text{Total score} = 10 + 4 = 14$$ 3. Calculate total maximum marks: $$\text{Total max marks} = 15 + 10 = 25$$ 4. Calculate the percentage scored by the student: $$\text{Percentage} = \frac{14}{25} \times 100 = 56\%$$ 5. Since the student scored 56%, which is more than 54%, the student passes the examination. --- 6. Problem 17: Solve the inequality $$2x - 1 \leq 11$$ 7. Add 1 to both sides: $$2x \leq 12$$ 8. Divide both sides by 2: $$x \leq 6$$ 9. Solution: All values of $x$ less than or equal to 6 satisfy the inequality. --- 10. Problem 18: Solve the equation $$1 \frac{1}{5} + \frac{22}{d} = 1 \frac{3}{4}$$ 11. Convert mixed numbers to improper fractions: $$1 \frac{1}{5} = \frac{6}{5}, \quad 1 \frac{3}{4} = \frac{7}{4}$$ 12. Substitute into equation: $$\frac{6}{5} + \frac{22}{d} = \frac{7}{4}$$ 13. Subtract $\frac{6}{5}$ from both sides: $$\frac{22}{d} = \frac{7}{4} - \frac{6}{5}$$ 14. Find common denominator and subtract: $$\frac{7}{4} - \frac{6}{5} = \frac{35}{20} - \frac{24}{20} = \frac{11}{20}$$ 15. So, $$\frac{22}{d} = \frac{11}{20}$$ 16. Cross multiply: $$22 \times 20 = 11 \times d$$ $$440 = 11d$$ 17. Divide both sides by 11: $$d = 40$$ 18. Final answer for $d$ is 40.