Question

Solve for n. (8n+6)/(4n+8)=1 Show your work here

Answer 1

To solve for n in the equation (8n+6)/(4n+8)=1, we multiply both sides by the denominator, simplify, and solve for n, which gives us n = 0.5. This solution is confirmed by plugging it back into the original equation.

Step-by-step explanation:

To solve for n, we have the equation (8n+6)/(4n+8)=1. To simplify this equation, we can multiply both sides by the denominator, 4n+8, to eliminate it. The equation then becomes 8n+6 = 4n+8. Subtracting 4n from both sides gives us 4n+6 = 8. Subtracting 6 from both sides gives us 4n = 2. Finally, dividing by 4, we find that n = 2 / 4, which simplifies to n = 0.5.

Let's check our work to ensure that this solution is reasonable. Plugging n = 0.5 into the original equation:

(8(0.5)+6)/(4(0.5)+8) = (4+6)/(2+8) = 10/10 = 1

Since the left side equals the right side when n = 0.5, our solution is correct. This step is important to eliminate any potential errors and confirm that the solution makes sense.

Answer 2

The value of n that satisfies the equation is n = 1/2.

Multiply both sides of the equation by the denominator (4n+8) to eliminate the fraction. This gives us:

(8n+6) = (4n+8)

Expand the brackets on both sides of the equation:

8n + 6 = 4n + 8

Simplify the equation by combining like terms. In this case, we can subtract 4n from both sides of the equation:

8n - 4n + 6 = 4n - 4n + 8

This simplifies to:

4n + 6 = 8

Now, subtract 6 from both sides of the equation:

4n + 6 - 6 = 8 - 6

This simplifies to:

4n = 2

Finally, divide both sides of the equation by 4 to isolate n:

(4n)/4 = 2/4

This simplifies to:

n = 1/2