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Solve for x. \newline(27)x=−14(\frac{2}{7})x= -14 \newline x=x = ______

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Q. Solve for x. \newline(27)x=−14(\frac{2}{7})x= -14 \newline x=x = ______
  1. Isolate the variable x: Isolate the variable x by multiplying both sides of the equation by the reciprocal of the coefficient of x.\newlineThe reciprocal of 27\frac{2}{7} is 72\frac{7}{2}. So, we multiply both sides of the equation by 72\frac{7}{2} to isolate x.\newline(72)⋅(27)x=(72)⋅−14\left(\frac{7}{2}\right) \cdot \left(\frac{2}{7}\right)x = \left(\frac{7}{2}\right) \cdot -14
  2. Simplify both sides: Simplify both sides of the equation.\newlineOn the left side, (72)×(27)(\frac{7}{2}) \times (\frac{2}{7}) simplifies to 11, leaving us with xx.\newlineOn the right side, (72)×−14(\frac{7}{2}) \times -14 simplifies to −49-49.\newlineSo, x=−49x = -49.
  3. Check the solution: Check the solution by substituting the value of xx back into the original equation.\newline(27)(−49)(\frac{2}{7})(-49) should equal −14-14.\newline(27)(−49)=−987=−14(\frac{2}{7})(-49) = \frac{-98}{7} = -14, which is true.

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