Solve and check: 24 + 3 (x + 2) = 5(x − 12).

Verified step by step guidance

1. Distribute the 3 on the left side: 24 + 3(x + 2) becomes 24 + 3x + 6.
2. Combine like terms on the left side: 24 + 6 becomes 30, so the equation is 3x + 30.
3. Distribute the 5 on the right side: 5(x - 12) becomes 5x - 60.
4. Set the equation: 3x + 30 = 5x - 60.
5. Rearrange the equation to isolate x: Subtract 3x from both sides to get 30 = 2x - 60, then add 60 to both sides to solve for x.

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term inside a parenthesis. In the given equation, applying the distributive property is essential to simplify expressions like 3(x + 2) and 5(x - 12) before solving for x.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying equations to isolate the variable. In the equation provided, after applying the distributive property, combining like terms will help in simplifying both sides of the equation to solve for x.

Isolating the Variable

Isolating the variable means rearranging the equation to get the variable (in this case, x) on one side and the constants on the other. This process often involves using inverse operations, such as addition, subtraction, multiplication, or division. Successfully isolating x will lead to the solution of the equation.