Question

Solve for u. 5=(1)/(u+6) Simplify your answer as much as possible.

Answer 1

To solve for u in the equation 5 = (1)/(u+6), multiply both sides by (u+6), distribute, subtract 30, and then divide by 5 to get u = -29/5 or -5.8, which checks out when substituted back into the original equation.

Step-by-step explanation:

To solve for u, start with the equation 5 = (1)/(u+6).

1. Multiply both sides of the equation by (u+6) to eliminate the denominator: 5(u+6) = 1.
2. Distribute 5 to both terms inside the parentheses: 5u + 30 = 1.
3. Subtract 30 from both sides to get 5u on one side: 5u = 1 - 30.
4. Simplify the right side: 5u = -29.
5. Finally, divide both sides by 5 to isolate u: u = -29/5.

So, the solution for u is u = -29/5 or -5.8.

Check the answer to see if it is reasonable by plugging it back into the original equation: 5 = 1/(-5.8+6). This simplifies to 5 = 1/0.2, which is correct since 1/0.2 = 5.