Solve each equation. (1/15)(2x+5) = (1/9)(x+2)

Verified step by step guidance

1. Start by writing the equation clearly: \(\frac{1}{15}(2x + 5) = \frac{1}{9}(x + 2)\).
2. To eliminate the fractions, multiply both sides of the equation by the least common denominator (LCD) of 15 and 9, which is 45.
3. Distribute the 45 to both sides: \(45 \times \frac{1}{15}(2x + 5) = 45 \times \frac{1}{9}(x + 2)\).
4. Simplify both sides by performing the multiplication: \$3(2x + 5) = 5(x + 2)$.
5. Next, distribute the 3 and 5 on each side: \$6x + 15 = 5x + 10\(. Then, solve for \)x$ by isolating the variable on one side.

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.

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, a(b + c) = ab + ac. This is essential for simplifying expressions before solving equations.

Working with Fractions in Equations

When equations involve fractions, it is important to handle them carefully by finding common denominators or multiplying both sides by the least common denominator to eliminate fractions, simplifying the solving process.