In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)

Verified step by step guidance

1. Distribute the 0.4 on the left side: 0.7x + 0.4 \times 20 = 0.5(x + 20).
2. Calculate 0.4 \times 20 to simplify the left side.
3. Distribute the 0.5 on the right side: 0.5x + 0.5 \times 20.
4. Calculate 0.5 \times 20 to simplify the right side.
5. Combine like terms and solve for x by isolating it on one side of the equation.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants. Understanding how to manipulate and solve these equations is fundamental in algebra, as they often model real-world situations.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by two or more terms inside a set of parentheses. This property is essential for simplifying expressions and solving equations, as it helps eliminate parentheses and combine like terms effectively.

Combining Like Terms

Combining like terms involves simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This process is crucial in solving equations, as it helps to reduce complexity and isolate the variable, making it easier to find the solution.