To solve equations with variables on each side, the goal is to isolate the variable on one side of the equation. Here's the general approach:

Steps to Solve:

1. Simplify both sides: Combine like terms on each side of the equation.
2. Move variables to one side: Use addition or subtraction to get all variables on one side.
3. Move constants to the other side: Use addition or subtraction to get all constant terms on the other side.
4. Solve for the variable: Divide or multiply to isolate the variable.

Example Problem:

Solve:
$3x + 5 = 2x - 7$

Step-by-Step Solution:

1. Move variables to one side: Subtract $2x$ from both sides. $3x - 2x + 5 = -7$ $x + 5 = -7$

2. Move constants to the other side: Subtract 5 from both sides. $x = -7 - 5$ $x = -12$

Solution:

$x = -12$

Another Example:

Solve:
$5x - 3 = 3x + 9$

Step-by-Step Solution:

1. Move variables to one side: Subtract $3x$ from both sides. $5x - 3x - 3 = 9$ $2x - 3 = 9$

2. Move constants to the other side: Add 3 to both sides. $2x = 9 + 3$ $2x = 12$

3. Solve for $x$: Divide by 2. $x = \frac{12}{2}$ $x = 6$

Solution:

$x = 6$

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Do you want more examples or explanations?

Related Questions:

1. How do you solve equations with fractions on each side?
2. What happens if the variables cancel out on both sides?
3. How do you solve equations involving parentheses?
4. Can you demonstrate solving equations with decimals?
5. How do you solve equations where the variable appears more than once on one side?

Tip: Always double-check your solution by substituting it back into the original equation to ensure both sides are equal.