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Math  /  Algebra

QuestionSolve 4(2n+5)=13n4(2 n+5)=13 n Give your answer as a whole number or as a decimal.

Studdy Solution

STEP 1

1. The equation 4(2n+5)=13n 4(2n + 5) = 13n is a linear equation in one variable.
2. The goal is to find the value of n n .
3. The equation involves basic algebraic operations, including distribution and combining like terms.

STEP 2

1. Expand the equation using the distributive property.
2. Move all terms involving n n to one side of the equation.
3. Solve for n n by isolating the variable.
4. Verify the solution by substituting it back into the original equation.

STEP 3

Apply the distributive property to the left side of the equation:
4(2n+5)=8n+20 4(2n + 5) = 8n + 20
So, the equation becomes:
8n+20=13n 8n + 20 = 13n

STEP 4

Move all terms involving n n to one side by subtracting 8n 8n from both sides:
8n+20−8n=13n−8n 8n + 20 - 8n = 13n - 8n
This simplifies to:
20=5n 20 = 5n

STEP 5

Solve for n n by dividing both sides by 5:
205=5n5 \frac{20}{5} = \frac{5n}{5}
This simplifies to:
n=4 n = 4

STEP 6

Verify the solution by substituting n=4 n = 4 back into the original equation:
Original equation: 4(2n+5)=13n 4(2n + 5) = 13n
Substitute n=4 n = 4 :
4(2(4)+5)=13(4) 4(2(4) + 5) = 13(4)
Simplify both sides:
4(8+5)=52 4(8 + 5) = 52
4(13)=52 4(13) = 52
Both sides are equal, confirming that the solution is correct.
The solution is:
4 \boxed{4}

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