Solve each linear equation. See Examples 1–3. 0.2x - 0.5 = 0.1x + 7

Verified step by step guidance

1. Start by writing down the given equation: \$0.2x - 0.5 = 0.1x + 7$.
2. To isolate the variable terms on one side, subtract \$0.1x\( from both sides: \)0.2x - 0.1x - 0.5 = 7$.
3. Simplify the left side by combining like terms: \((0.2 - 0.1)x - 0.5 = 7\) which becomes \$0.1x - 0.5 = 7$.
4. Next, add \(0.5\) to both sides to move the constant term: \$0.1x = 7 + 0.5$.
5. Finally, divide both sides by \(0.1\) to solve for \(x\): \(x = \frac{7 + 0.5}{0.1}\).

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 goal is to find the value of the variable that makes the equation true. In this problem, the equation involves the variable x with coefficients and constants.

Isolating the Variable

To solve a linear equation, you need to isolate the variable on one side of the equation. This involves using inverse operations such as addition, subtraction, multiplication, or division to simplify the equation step-by-step until the variable stands alone.

Combining Like Terms

Combining like terms means adding or subtracting terms that have the same variable raised to the same power. This simplifies the equation and makes it easier to isolate the variable. In this problem, terms involving x and constants should be grouped appropriately.