Solve each equation. 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: \((0.2x - 0.1x) - 0.5 = 7\) 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

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side by performing inverse operations such as addition, subtraction, multiplication, or division.

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 helps to reduce the equation to a simpler form, making it easier to solve.

Working with Decimals in Equations

When solving equations with decimals, it is important to carefully perform arithmetic operations to maintain accuracy. Understanding how to add, subtract, multiply, and divide decimals ensures correct manipulation of terms during the solution process.