Solution: Substitute $ a = 5 $ into $ 5(5 + b) = 120 $. Simplify: $ 25 + 5b = 120 $. Subtract 25: $ 5b = 95 $. Divide by 5: $ b = 19 $. - Decision Point
How to Solve the Equation $ 5(5 + b) = 120 $: A Step-by-Step Guide
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:
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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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$$
25 + 5b = 120
$$
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:
