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Solve Equations with Variables on Both Sides Quick Check

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Sure! To solve equations with variables on both sides, you can follow these general steps:

  1. Simplify both sides: If there are parentheses, distribute them. Combine like terms where possible.

  2. Move the variable terms to one side: You can do this by adding or subtracting the variable terms from both sides of the equation.

  3. Move the constant terms to the other side: Again, use addition or subtraction to isolate the constant terms.

  4. 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.

  5. 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

  1. \( 4x + 10 = 2x + 26 \)
  2. \( 5y - 3 = 2y + 12 \)
  3. \( 7 - 3a = 2a + 1 \)

Feel free to ask for the solutions to these equations or any others you have!