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:

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

Understanding the Context

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:

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

Key Insights

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

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:

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Final Thoughts

$$
25 + 5b = 120
$$

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: