Subjects algebra

Solve Fraction Equation Afc161

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1. **State the problem:** Solve for the unknown value represented by "?" in the equation $$\frac{5}{12} - ? + \frac{5}{4} = \frac{2}{3}$$. 2. **Isolate the unknown:** We want to find the value of "?". Rearrange the equation to isolate "?": $$\frac{5}{12} - ? + \frac{5}{4} = \frac{2}{3} \implies -? = \frac{2}{3} - \frac{5}{12} - \frac{5}{4}$$ 3. **Find a common denominator:** The denominators are 3, 12, and 4. The least common denominator (LCD) is 12. 4. **Convert each fraction to have denominator 12:** $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$$ 5. **Substitute back:** $$-? = \frac{8}{12} - \frac{5}{12} - \frac{15}{12}$$ 6. **Combine the fractions:** $$-? = \frac{8 - 5 - 15}{12} = \frac{-12}{12}$$ 7. **Simplify the fraction:** $$-? = \frac{\cancel{-12}}{\cancel{12}} = -1$$ 8. **Solve for ? by multiplying both sides by -1:** $$? = 1$$ **Final answer:** $$? = 1$$