Solve the equation for x: (2x-3)/5 = x/10
x = 2.
To solve the equation (2x - 3)/5 = x/10, we can multiply both sides by 10 to eliminate the denominators, leading us to the solution x = 2.
This is the correct solution. By substituting x = 2 back into the original equation, we find that both sides equal 0.4, confirming that x = 2 satisfies the equation.
If we substitute x = 3 into the equation, we get (2(3) - 3)/5 = 3/10, which simplifies to 3/5 = 3/10. This statement is false, as 3/5 does not equal 3/10.
Substituting x = 15 results in (2(15) - 3)/5 = 15/10, which simplifies to (30 - 3)/5 = 15/10. This simplifies to 27/5 = 15/10, which is incorrect, as 27/5 does not equal 15/10.
If we substitute x = 10, we find (2(10) - 3)/5 = 10/10, which leads to (20 - 3)/5 = 1. This simplifies to 17/5 = 1, which is also incorrect since 17/5 is not equal to 1.
The equation (2x - 3)/5 = x/10 simplifies to reveal that the only valid solution is x = 2. Other choices do not satisfy the original equation, as demonstrated through substitution, confirming that only option A is correct. This process highlights the importance of checking solutions in algebraic equations to ensure accuracy.
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