Solve 8(1900 - 1.5x) + 10(1400 - 1.5x) = 25x.

Step-by-step solution

1. 1

   Distribute over both brackets. Nothing can be combined while the $x$ is trapped inside parentheses, so multiply through first: $8\cdot 1900 - 8\cdot 1.5x + 10\cdot 1400 - 10\cdot 1.5x = 25x$ $15200 - 12x + 14000 - 15x = 25x.$

2. 2

   Collect the constants and the x-terms on the left. $15200 + 14000 = 29200$ and $-12x - 15x = -27x$, so the equation becomes $29200 - 27x = 25x.$ Both bracket terms subtract $x$, so the coefficients add rather than cancel.

3. 3

   Gather all x on one side. Add $27x$ to both sides so the coefficient stays positive and no sign error creeps in: $29200 = 52x.$

4. 4

   Divide by the coefficient of x. $x = \frac{29200}{52} = \frac{7300}{13} \approx 561.54,$ after dividing numerator and denominator by $4$. The result is not a terminating decimal, so the fraction $\tfrac{7300}{13}$ is the exact answer.

5. 5

   Verify by substitution. With $x = \tfrac{7300}{13}$, $1.5x = \tfrac{10950}{13}$, so $1900 - 1.5x = \tfrac{13750}{13}$ and $1400 - 1.5x = \tfrac{7250}{13}$. Then $8\cdot\tfrac{13750}{13} + 10\cdot\tfrac{7250}{13} = \tfrac{110000+72500}{13} = \tfrac{182500}{13}$, and $25\cdot\tfrac{7300}{13} = \tfrac{182500}{13}$ - the two sides match exactly.