Solve each equation for x. ax+b=3(x-a)

Verified step by step guidance

1. Start with the given equation: \(ax + b = 3(x - a)\).
2. Distribute the 3 on the right side to both terms inside the parentheses: \(ax + b = 3x - 3a\).
3. Get all terms involving \(x\) on one side and constants on the other side. Subtract \$3x\( from both sides and subtract \)b\( from both sides: \)ax - 3x = -3a - b$.
4. Factor out \(x\) on the left side: \(x(a - 3) = -3a - b\).
5. Divide both sides by \((a - 3)\) to isolate \(x\): \(x = \frac{-3a - b}{a - 3}\).

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, in 3(x - a), you multiply 3 by x and 3 by -a, resulting in 3x - 3a. This step is essential to simplify and solve the equation.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. After distributing, you group terms with x on one side and constants on the other to simplify the equation and isolate the variable.

Solving Linear Equations

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