To solve equations with variables on both sides, follow these steps:

General Steps:

1. Simplify both sides: Combine like terms on each side of the equation if needed.
2. Move the variables to one side: Use addition or subtraction to get all the terms with variables on one side of the equation.
3. Move the constants to the other side: Use addition or subtraction to isolate the variable term.
4. Solve for the variable: Divide or multiply as needed to find the value of the variable.
5. Check your solution: Substitute your solution back into the original equation to ensure it works.

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Example:

Solve: $3x + 5 = 2x + 10$

1. Simplify both sides: No further simplification is needed here.

2. Move the variables to one side: Subtract $2x$ from both sides: $3x - 2x + 5 = 10$ Simplify: $x + 5 = 10$

3. Move the constants to the other side: Subtract 5 from both sides: $x = 10 - 5$ Simplify: $x = 5$

4. Check the solution: Substitute $x = 5$ back into the original equation: $3(5) + 5 = 2(5) + 10$ Simplify: $15 + 5 = 10 + 10$ $20 = 20$ Since both sides are equal, the solution is correct.

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Key Tips:

• Always perform the same operation on both sides of the equation to maintain balance.
• Double-check your solution by substituting it back into the original equation.

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Want to try similar examples?

1. Solve $4x - 7 = 2x + 1$.
2. Solve $5y + 8 = 3y - 4$.
3. Solve $2m + 3 = 4m - 5$.
4. Solve $7k - 6 = 2k + 9$.
5. Solve $6p + 2 = 5p + 10$.

Tip: If fractions appear, clear them first by multiplying through by the denominator to simplify the equation.