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

Verified step by step guidance

1. Distribute the 0.06 to both terms inside the parentheses in the expression 0.06(x+12), rewriting the equation as \(0.08x + 0.06x + 0.06 \times 12 = 7.72\).
2. Simplify the multiplication \(0.06 \times 12\) to get a constant term, and combine like terms involving \(x\) by adding \$0.08x\( and \)0.06x$.
3. Rewrite the equation in the form \(ax + b = c\), where \(a\) is the sum of the coefficients of \(x\), \(b\) is the constant term from the previous step, and \(c\) is 7.72.
4. Isolate the variable term by subtracting the constant term \(b\) from both sides of the equation to get \(ax = c - b\).
5. Solve for \(x\) by dividing both sides of the equation by the coefficient \(a\), resulting in \(x = \frac{c - b}{a}\).

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This is essential for expanding expressions like 0.06(x + 12) before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. After distributing, terms with 'x' can be combined to simplify the equation, making it easier to isolate the variable.

Solving Linear Equations

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