Solve each equation. 0.08x+0.06(x+12) = 7.72

Verified step by step guidance

1. Distribute the 0.06 across the terms inside the parentheses: $0.06(x+12)=0.06x+0.72$.
2. Rewrite the equation with the distributed terms: $0.08x+0.06x+0.72=7.72$.
3. Combine like terms on the left side: $0.08x+0.06x=0.14x$, so the equation becomes $0.14x+0.72=7.72$.
4. Subtract 0.72 from both sides to isolate the term with $x$: $0.14x=7.72-0.72$.
5. Divide both sides by 0.14 to solve for $x$: $x=\frac{7.00}{0.14}$.

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 linear equations is essential for finding the value of the variable, in this case, x.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows you to multiply a single term by each term within a set of parentheses. In the given equation, applying the distributive property to 0.06(x + 12) is crucial for simplifying the equation and isolating the variable.

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 step is important in solving equations, as it helps to reduce the equation to a simpler form, making it easier to isolate the variable and find its value.