Solution: Substitute $ a = 5 $ into $ 5(5 + b) = 120 $. Simplify: $ 25 + 5b = 120 $. Subtract 25: $ 5b = 95 $. Divide by 5: $ b = 19 $.

February 22, 2026

How to Solve the Equation $ 5(5 + b) = 120 $: A Step-by-Step Guide

Solving linear equations efficiently is a key skill in algebra, and one of the most common types involves substitution and simplification. One such example is solving the equation:

$$ 5(5 + b) = 120 $$

This equation is easy to tackle when broken down step by step. In particular, substituting $ a = 5 $ simplifies the expression cleanly and leads directly to the solution. Let’s walk through the process.

Step 1: Apply the substitution

Start by substituting $ a = 5 $ into the original equation:

$$ 5(5 + b) = 120 $$

Here, $ a $ represents the constant 5, making this step simple: $ 5(5 + b) $ becomes the left-hand side before substituting.

Step 2: Simplify the equation

Distribute the 5 inside the parentheses:

$$ 25 + 5b = 120 $$

Now the equation clearly shows the constant and variable terms, ready for the next step.

Step 3: Isolate the variable term

Subtract 25 from both sides to eliminate the constant on the left:

$$ 5b = 120 - 25 $$ $$ 5b = 95 $$

This reduces the equation to a simple form where the variable $ b $ can be isolated.

Step 4: Solve for $ b $

Divide both sides by 5:

$$ b = rac{95}{5} $$ $$ b = 19 $$

Final Answer

The solution to the equation $ 5(5 + b) = 120 $ is $ oxed{b = 19} $.

Why This Method Works

Using substitution with a known value simplifies algebraic expressions, especially when combining constants early. Breaking the process into clear steps—substitution, simplification, isolation, and solution—makes complex equations approachable. This method is essential not just for homework, but also in real-world problem-solving where clarity and speed matter.

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Optimizing your understanding of substitution and simplification strengthens your algebraic foundation and boosts confidence in tackling more complex math problems.