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(85)x=32(\frac{8}{5})x= 32

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Full solution

Q. (85)x=32(\frac{8}{5})x= 32
  1. Identify equation for x: Identify the equation to solve for x.\newlineWe have the equation (85)x=32(\frac{8}{5})x = 32, and we need to find the value of xx.
  2. Isolate x by multiplying: Isolate xx by multiplying both sides of the equation by the reciprocal of (85)(\frac{8}{5}).\newlineTo isolate xx, we multiply both sides by 58\frac{5}{8}, which is the reciprocal of 85\frac{8}{5}.
  3. Perform multiplication on both sides: Perform the multiplication on both sides. (58)×(85)x=(58)×32(\frac{5}{8}) \times (\frac{8}{5})x = (\frac{5}{8}) \times 32
  4. Simplify both sides: Simplify both sides of the equation.\newlineThe left side simplifies to xx because (58)⋅(85)=1(\frac{5}{8}) \cdot (\frac{8}{5}) = 1. The right side is 5⋅325 \cdot 32 divided by 88.
  5. Calculate right side: Calculate the right side of the equation.\newline5×32=1605 \times 32 = 160, and 160÷8=20160 \div 8 = 20. So, x=20x = 20.

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