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Question

Difficulty: EasyLinear Equations in One Variable

If 3(2n−5)=4n+93(2n - 5) = 4n + 9, what is the value of nn?

Answer: 12

Answer

12
To solve the equation 3(2n−5)=4n+93(2n - 5) = 4n + 9, we first distribute the 3 to the terms inside the parentheses to get 6n−15=4n+96n - 15 = 4n + 9. Next, we subtract 4n4n from both sides to group the variable terms, giving 2n−15=92n - 15 = 9. We then add 15 to both sides to isolate the variable term, resulting in 2n=242n = 24. Finally, dividing both sides by 2 gives the solution n=12n = 12.

Step-by-Step Solution

1
Distribute 3 to the terms inside the parentheses.
6n−15=4n+96n - 15 = 4n + 9
To simplify the left side of the equation and remove parentheses.
2
Subtract 4n4n from both sides of the equation.
2n−15=92n - 15 = 9
To group the variable terms on one side of the equation.
3
Add 15 to both sides of the equation.
2n=242n = 24
To isolate the term with the variable nn.
4
Divide both sides of the equation by 2.
n=12n = 12
To solve for nn.

Key Concept

Solving a linear equation in one variable by applying the distributive property and isolating the variable.
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Topics

Linear Equations in One Variable

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