Final answer:
The algebraic equation 8.2(6x-3) - 7(7x-1.2) has one solution, which is x = 81. This is derived by expanding the equation, simplifying, and solving for x.
Step-by-step explanation:
The question is asking to determine the number of solutions to the algebraic equation 8.2(6x-3) - 7(7x-1.2).
To solve this, let's first expand the equation:
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- 8.2 * 6x - 8.2 * 3 = 49.2x - 24.6
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- - (7 * 7x - 7 * 1.2) = -49x + 8.4
Combine like terms:
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- 49.2x - 49x = 0.2x
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- -24.6 + 8.4 = -16.2
Now we have 0.2x - 16.2 = 0. Solving for x:
Since we found a single value for x, this equation has one solution. Always check to see if the solution is reasonable by substituting back into the original equation.