Question

Solve Equations with Variables on Both Sides Quick Check

Answer 1

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!