Solve each equation. 2x+8 = 3x+2

Verified step by step guidance

1. Start with the given equation: \$2x + 8 = 3x + 2$.
2. To isolate the variable terms on one side, subtract \$2x\( from both sides: \)2x + 8 - 2x = 3x + 2 - 2x\(, which simplifies to \)8 = x + 2$.
3. Next, isolate \(x\) by subtracting \$2\( from both sides: \)8 - 2 = x + 2 - 2\(, which simplifies to \)6 = x$.
4. Rewrite the solution as \(x = 6\) to clearly state the value of the variable.
5. Verify the solution by substituting \(x = 6\) back into the original equation to ensure both sides are equal.

Key Concepts

Solving Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Solving such equations involves isolating the variable on one side to find its value. This often requires performing inverse operations like addition, subtraction, multiplication, or division.

Properties of Equality

The properties of equality allow you to manipulate equations without changing their solutions. These include adding, subtracting, multiplying, or dividing both sides of an equation by the same number. Using these properties ensures the equation remains balanced while isolating the variable.

Combining Like Terms

Combining like terms means simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This step is essential to simplify both sides of the equation before isolating the variable, making the equation easier to solve.