2D + D + 1 = sin(2x) question of linear equation with constant coefficients
Understand the Problem
The question is asking to solve the linear equation expressed as 2D + D + 1 = sin(2x), where D is a variable with constant coefficients, and will require isolating D in terms of sin(2x).
Answer
$$ D = \frac{\sin(2x) - 1}{3} $$
Answer for screen readers
The solution for ( D ) in terms of ( \sin(2x) ) is: $$ D = \frac{\sin(2x) - 1}{3} $$
Steps to Solve
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Combine Like Terms First, combine the terms containing ( D ) on the left side of the equation. This gives us: $$ 3D + 1 = \sin(2x) $$
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Isolate the Variable D Next, subtract 1 from both sides of the equation to isolate ( 3D ): $$ 3D = \sin(2x) - 1 $$
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Solve for D Now, divide both sides of the equation by 3 to solve for ( D ): $$ D = \frac{\sin(2x) - 1}{3} $$
The solution for ( D ) in terms of ( \sin(2x) ) is: $$ D = \frac{\sin(2x) - 1}{3} $$
More Information
This equation shows how the variable ( D ) is expressed in relation to ( \sin(2x) ). The division by 3 balances the equation, ensuring that both sides remain equivalent.
Tips
- Forgetting to combine like terms: Ensure that you accurately combine terms involving ( D ) before proceeding with isolating it.
- Neglecting to apply the correct arithmetic operations: Make sure to perform addition and subtraction steps correctly when isolating the variable.
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