Sure! To solve equations with variables on both sides, you can follow these general steps:
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Simplify both sides: If there are parentheses, distribute them. Combine like terms where possible.
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Move the variable terms to one side: You can do this by adding or subtracting the variable terms from both sides of the equation.
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Move the constant terms to the other side: Again, use addition or subtraction to isolate the constant terms.
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Isolate the variable: If there’s still a coefficient in front of the variable, divide or multiply both sides by that number to solve for the variable.
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Check your solution: Substitute your solution back into the original equation to ensure both sides are equal.
Example
Let’s solve the following equation:
Example 1: \[ 3x + 5 = 2x + 12 \]
Step 1: Move the variable terms to one side. \[ 3x - 2x = 12 - 5 \] \[ x = 7 \]
Step 2: Check the solution by substituting \( x = 7 \) back into the original equation: \[ 3(7) + 5 = 2(7) + 12 \] \[ 21 + 5 = 14 + 12 \] \[ 26 = 26 \] (True)
More Practice Problems
- \( 4x + 10 = 2x + 26 \)
- \( 5y - 3 = 2y + 12 \)
- \( 7 - 3a = 2a + 1 \)
Feel free to ask for the solutions to these equations or any others you have!