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

Verified step by step guidance

1. Start by identifying the equation: \(2x + 8 = 3x + 2\).
2. To isolate the variable \(x\), first subtract \(2x\) from both sides of the equation to get \(8 = x + 2\).
3. Next, subtract \(2\) from both sides to isolate \(x\) on one side, resulting in \(x = 6\).
4. Verify your solution by substituting \(x = 6\) back into the original equation to ensure both sides are equal.
5. If both sides of the equation are equal after substitution, then \(x = 6\) is the correct solution.

Key Concepts

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. The general form is ax + b = c, where a, b, and c are constants. Solving linear equations involves finding the value of the variable that makes the equation true.

Isolating the Variable

Isolating the variable is a key step in solving equations, where the goal is to get the variable on one side of the equation and all other terms on the opposite side. This often involves performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation to maintain equality.

Balancing Equations

Balancing equations is the principle that states that both sides of an equation must remain equal after performing the same operation on both sides. This is crucial in solving equations, as it ensures that any manipulation does not change the equality, allowing for the correct solution to be found.