help mi ----- Nội dung dịch tự động từ ảnh ----- = [(x)]-중(4 ++ [G++ )] +
3 trả lời
30 Tham khảo câu trả lời từ Trợ lý ảo Lazi Sure, I'll help you solve these equations. ### Equation (e): \[ x \left( \frac{17}{2} - \left( -\frac{3}{7} + \frac{5}{3} \right) \right) = -\frac{1}{3} \] First, simplify the expression inside the parentheses: \[ -\frac{3}{7} + \frac{5}{3} \] To add these fractions, find a common denominator. The least common multiple of 7 and 3 is 21: \[ -\frac{3}{7} = -\frac{3 \times 3}{7 \times 3} = -\frac{9}{21} \] \[ \frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21} \] Now add the fractions: \[ -\frac{9}{21} + \frac{35}{21} = \frac{35 - 9}{21} = \frac{26}{21} \] So the equation becomes: \[ x \left( \frac{17}{2} - \frac{26}{21} \right) = -\frac{1}{3} \] Next, find a common denominator for the fractions inside the parentheses. The least common multiple of 2 and 21 is 42: \[ \frac{17}{2} = \frac{17 \times 21}{2 \times 21} = \frac{357}{42} \] \[ \frac{26}{21} = \frac{26 \times 2}{21 \times 2} = \frac{52}{42} \] Now subtract the fractions: \[ \frac{357}{42} - \frac{52}{42} = \frac{357 - 52}{42} = \frac{305}{42} \] So the equation is now: \[ x \left( \frac{305}{42} \right) = -\frac{1}{3} \] Solve for \( x \): \[ x = -\frac{1}{3} \div \frac{305}{42} = -\frac{1}{3} \times \frac{42}{305} = -\frac{42}{915} = -\frac{14}{305} \] ### Equation (f): \[ \frac{9}{2} - \left[ \frac{2}{3} - \left( x + \frac{7}{4} \right) \right] = \frac{5}{4} \] First, simplify the expression inside the parentheses: \[ \frac{2}{3} - \left( x + \frac{7}{4} \right) \] To subtract these, find a common denominator. The least common multiple of 3 and 4 is 12: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \] \[ \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \] So the expression becomes: \[ \frac{8}{12} - \left( x + \frac{21}{12} \right) = \frac{8}{12} - x - \frac{21}{12} = -x + \frac{8 - 21}{12} = -x - \frac{13}{12} \] Now the equation is: \[ \frac{9}{2} - \left( -x - \frac{13}{12} \right) = \frac{5}{4} \] Simplify the equation: \[ \frac{9}{2} + x + \frac{13}{12} = \frac{5}{4} \] Find a common denominator for the fractions. The least common multiple of 2, 12, and 4 is 12: \[ \frac{9}{2} = \frac{9 \times 6}{2 \times 6} = \frac{54}{12} \] \[ \frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12} \] So the equation becomes: \[ \frac{54}{12} + x + \frac{13}{12} = \frac{15}{12} \] Combine the fractions on the left side: \[ \frac{54 + 13}{12} + x = \frac{15}{12} \] \[ \frac{67}{12} + x = \frac{15}{12} \] Subtract \(\frac{67}{12}\) from both sides: \[ x = \frac{15}{12} - \frac{67}{12} \] \[ x = \frac{15 - 67}{12} \] \[ x = \frac{-52}{12} \] \[ x = -\frac{13}{3} \] So the solutions are: \[ x = -\frac{14}{305} \] \[ x = -\frac{13}{3} \]